The particle filter (PF) offers significant advantages over other nonlinear filters for non-Gaussian systems. However, it suffers from particle degeneracy and impoverishment, which can lead to deteriorated estimation performance. Through analyzing the filtering and Lamarckian evolution processes in this paper, we develop a Lamarckian PF (LPF), based on the assertion that specific characteristics of an organism are inheritable directly by its offspring. The LPF thus uses an overriding operator for the offspring to inherit traits such that the particle impoverishment problem is mitigated and filtering performance improved. Compared with the generic PF and the latest PF improved by differential evolution (DEPF), the LPF approximates posterior distribution more sufficiently. Meanwhile, the LPF weakens the impact of algorithmic parameters. Measured against the DEPF, the LPF reduces the complexity and improves the filtering speed and accuracy at the same time. Experimental results verify the validity and advantages of this new nonlinear filter.