Abstract: We proved the approximate controllability of a class of one-dimensional semilinear degenerate parabolic equations with boundary control functions by using the Kakutani fixed point theorem. The boundary condition of the problem at the degenerate point x=0 to be controlled is the second boundary condition in the sense of limit, and the boundary condition is the homogeneous Dirichlet condition at the non degenerate point x=1.

Key words: degenerate parabolic equation, approximate controllability, semilinear equation