Consider a class of p(x)-Kirchhoff type equations of the form $$left{-Mleft({int}_{Omega};frac{1}{p(x)}{mid}{ abla}u{mid}^{p(x)};dx ight);div;({mid}{ abla}u{mid}^{p(x)-2}{ abla}u)={lambda}V(x){mid}u{mid}^{q(x)-2}u;in;{Omega},\u=0;on;{partial}{Omega},$$ where p(x), $q(x){in}C({ar{Omega}})$ with 1 < $p^-;:=inf_{Omega};p(x){leq}p^+;:=sup_{Omega}p(x)$ < N, $M:{mathbb{R}}^+{ ightarrow}{mathbb{R}}^+$ is a continuous function that may be degenerate at zero, ${lambda}$ is a positive parameter. Using variational method, we obtain some existence and multiplicity results for such problem in two cases when the weight function V (x) may change sign or not.