In this paper, a class of chaotic maps with parameter q are introduced and bifurcations and chaos in proposed maps are numerical and analytical studied. Euler method is employed to get the continuous systems corresponding to chaotic maps and the fractional styles in Caputo's definition. Based on that, we finally infer a class of chaotic maps with the Adams–Bashforth–Moulton predictor-corrector method. In the simulation and analysis, we discuss the Logistic map with q and Hénon map with q, observe the route from period to chaos and do tests to analyze properties of maps with parameter q.