To better explore the robustness against cascading failures on complex networks, according to the redistribution rule of the real networks always lie between global preferential rule and local preferential rule or between even shared rule and extremely heterogeneous rule. A new cascading model is proposed based on a tunable load redistribution model. It can tune the load redistribution range and the redistribution heterogeneity of extra load respectively by a redistribution range coefficient and a redistribution heterogeneity coefficient. With this model, we further investigate cascading failures on scale-free networks in terms of numerical simulation and theoretical analysis respectively. Numerical simulation and analytic results show that the model can achieve better robustness against cascading failure than the previous model by adjusting the redistribution range and heterogeneity.