Traditional space-time adaptive processing (STAP) algorithm does not only have a big computation, but also cannot suppress the multiple narrowband jammer and the narrowband jammer which come from the same direction with the useful signal. To deal with these problems, an improved GPS anti-jam multistage nested Wiener filter (MSNWF) method which combines with multistage IIR lattice notch filter is proposed. The narrow-band jammer can be forecast and suppressed by using IIR lattice notch filter. The amount of computation can be reduced by using the improved MSNWF. The new method which can not only suppress both narrowband and broadband jammer effectively, but also improve the computation speed and SINR.