Abstract: The Fekete-Szego inequality for a subclass H（α,λ,A,B） of the class H of normalized analytic functions is studied.For each f（z）=z+∞∑n=2α_nzⁿ ∈ H（α,λ,A,B）,the sharp upper bounds of |α₃-α₂²|for any complex parameter u are obtained by using the fundamental inequalities of analytic functions and analytical techniques and the applications of the inequality of functions defined with Hadaniard product are proved. 

Key words: univalent function; H（α,λ,A,B） function, Fekete-Szeg\"{o} inequality