Particle filters has become a standard tool for state estimation in nonlinear systems. However, their performance usually deteriorates if the dimension of state space is high or the measurements are highly informative. A major challenge is to construct a proposal density that is well matched to the posterior distribution. Particle flow methods are a promising option for addressing this task. In this paper, we develop a particle flow particle filter algorithm to address the case where both the process noise and the measurement noise are distributed as mixtures of Gaussians. Numerical experiments are performed to explore when the proposed method offers advantages compared to existing techniques.