This article is from the James Bond FAQ, by Michael Reed firstname.lastname@example.org with numerous contributions by others.
No, but readers were meant to think so upon its initial release. At the end
of the book, Bond falls to the ground having been stabbed with Rosa Klebb's
shoe knife. It was often reported that Fleming intended to kill off James
Bond, and his contemporary, author Raymond Chandler, talked him out of it.
While the book had an intentional cliffhanger, the idea it was the end of
Bond is an oft-reported myth.
Some sources suggest Fleming never gave a moment's thought to ending the
series, and other merely that he was bored and left his options open. As far
as the Chandler story, the truth was that Chandler was asked to review the
previous book, "Diamonds Are Forever", and suggested that Fleming could, and
should, do better. Fleming was inspired by the criticism and completed
"Russia". He originally had Bond and Tatiana end up together but near the
end of completing it he changed the final scene to the published version.
But that seems to be more to stimulate interest than to kill James Bond.
That May, according to Andrew Lycett's thorough biography, Fleming received
a letter from Geoffrey Boothroyd (see Brief 4 Section 2 for details) and by
August Fleming had promised to include Boothroyd's ideas in the "next"
adventure he would write, which became "Doctor No". At the time he was
completing the final cover design for the unreleased "Russia", among other
projects. While he was concerned personal matters would interfere with his
writing schedule the following year, Fleming knew he would be writing a new
Bond novel to continue his series.