A constructing approach to generating N×M-scroll attractors with polynomial and step function is reported. In Chuas circuit, only two or three scrolls can be generated by traditional polynomial function. On this basis, the multi-scroll of x direction in phase space is obtained by polynomial shift. And then the saddle-focus equilibrium points with index-2 in phase space are extended by combining both polynomial and step function, which makes it possible to extend the multi-scroll in y direction. Then the grid multi-scroll chaotic attractors are generated. The main feature of this constructing approach is generating grid multi-scroll chaotic attractors by combining both smooth curves and non-smooth curves for the first time. And the arbitrary planar grid multi-scroll chaotic attractors array can be generated by adjusting the values of natural numbers N and M. The effectiveness of this method has been verified by theoretical analysis, numerical simulation and circuit simulation.