The mass transport processes always accompanies the flow phenomena and have attracted many researches. A lot of numerical methods have been developed to study them. These numerical methods can be classified into the Eulerian and the Lagrangian approaches. The Lagrangian approach has advantages in high stability and simplicity over the Eulerian approach, but suffers from heavy computational cost. In this paper, we are mainly concerned with the trade-offs between the accuracy and computational cost when applying the random walk method, which is a Lagrangian approach for examining the mass transport scenario. We introduce a linear model to assess the accuracy of the random walk method in several computational configurations. Studies on computational parameters, i.e. the size of time step and number of particles, are conducted with the focus on estimation of the longitudinal dispersion coefficient in steady flows. The results show that the proposed linear model can satisfactorily explain the computational accuracy, both in sample and out-of-sample. Furthermore, we find a constant dimensionless parameter, which quantifies a generic relationship between the accuracy and the number of particles regardless of the flow and diffusion conditions. This dimensionless parameter is of theoretic value and offers guidelines for choosing the correct computational parameters to achieve the required numerical accuracy.