The 64-year-old Maryland native, detained at Havana's Jose Marti International Airport Dec. 3, 2009, said in his letter, to be delivered to the White House Tuesday: "As I reflect on these last four years, I find myself asking the same question -- why? Why am I still here?"
Gross was working as a U.S. Agency for International Development contractor, bringing satellite phones, smartphones and computer equipment to members of Cuba's Jewish community when he was arrested.
The Castro regime said he had no permit to bring the equipment into the country.
Gross was convicted March 12, 2011, of crimes against the Cuban state and sentenced to 15 years in prison.
The official Prensa Latina news agency called his alleged crimes part of a "subversive project of the U.S. government that aimed to destroy the [Cuban] revolution through the use of communication systems out of the control of authorities."
The U.S. State Department has said Gross is "unjustly jailed" and called for his release. But Obama has sent no special emissaries or agreed to negotiate over him.
"With the utmost respect, Mr. President, I fear that my government -- the very government I was serving when I began this nightmare -- has abandoned me," Gross said in the letter, copy of which was provided to The Washington Post in advance of its White House delivery.
"Officials in your administration have expressed sympathy and called for my unconditional release, and I very much appreciate that. But it has not brought me home," Gross said.
"It is clear to me, Mr. President, that only with your personal involvement can my release be secured," he continued.
"I know that your administration and prior administrations have taken extraordinary steps to obtain the release of other U.S. citizens imprisoned abroad -- even citizens who were not arrested for their work on behalf of their country. I ask that you also take action to secure my release, for my sake and for the sake of my family," he said.
But more than just for him, Gross added, "All Americans around the world, military and civilian, "must not harbor any doubt that if they are taken captive in a foreign land, our government will move heaven and earth to secure their freedom."
Gross' wife, Judy Gross, who has criticized Obama and U.S. policy toward Cuba, planned to lead a demonstration outside the White House in her husband's behalf Tuesday.
The Grosses' disillusionment over what they call the administration's lackluster efforts to free him has U.S. lawmaker support.
A bipartisan group of 66 senators, led by Patrick Leahy, D-Vt., said in a letter to Obama last month Gross' case was "a matter of grave urgency."
The senators urged Obama to "act expeditiously to take whatever steps are in the national interest to obtain his release" and said they stood "ready to support your administration in pursuit of this worthy goal."
Gross' attorney, Scott Gilbert, told the Post Cuban officials "have made very clear to the United States, and to us directly to pass on, that they're willing to sit down and meet with no preconditions to discuss Alan's release."
U.S. Assistant Secretary of State for Western Hemisphere Affairs Roberta Jacobson blamed Cuba for the lack of movement in Gross' case.
"Some very senior people in this administration have put their minds and attention on trying to get Alan Gross out of prison, as well as some senior members of Congress. In the end, it is up to the Cubans, and they have not been responsive," she said in remarks quoted by the Post.
"We continue to urge the Cuban government to release him immediately," she said.