Abstract: A new type of explicit difference schemes, the stable criterion of which is free from time step τ and space grid length d, is presented. Its stability is only determined by me=τ/d e(e=1,2,3),the positive integer part of τλe/dλe,where λ1=u+c, λ3=u-c denotes the eastward and westward gravity wave speed respectively, and λ2=u denotes Rossby wave speed.As a numerical test of the present schemes, equations (3.15), (3.16) and (3.17) were used in solving one-dimensional shallow water wave equation, with d=25 km and τ=20 minute. Table 1,Figs 3(1-3) and Figs 4(1-3) shows the examples of the calculated results.