For the estimation problem that the RBPF-SLAM algorithm used in mobile robots suffers from sample impoverishment in grid mapping, a Gaussian distributed resampling(GDR) based RBPF-SLAM algorithm is proposed. Firstly, the improved algorithm sorts particles according to the weight size. Furthermore, Gaussian distributed resampling is applied to disperse the high-weight particles so as to generate new particles. By using GDR, particle diversity can be maintained and sample impoverishment can be avoided. Thus accurate grid mapping is guaranteed. Experimental results show the effectiveness of the proposed algorithm. Meanwhile, the results prove that the proposed algorithm guarantees reliable estimation with less samples, and the computation burden can be reduced efficiently.