Developments in tissue engineering over the past decade have offered promising future for the repair and reconstruction of damaged tissues. To regenerate three dimensional and weight-bearing implants, advances in biomaterials and manufacturing technologies prompted cell cultivations with natural or artificial scaffolds, in which cells are allowed to proliferate, migrate, and differentiate in vitro. In this article, we develop a mathematical model for cell growth in a porous scaffold. By treating the cell-scaffold construct as a porous medium, a continuum model is set up based on basic principles of mass conservation. In addition to cell growth kinetics, we incorporate cell diffusion in the model to describe the effects of cell random walks. Computational results are compared to experimental data found in the literature. With this model, we are able to investigate cell motility, heterogeneous cell distributions, and non-uniform seeding for tissue engineering applications. Results show that random walks tend to enhance uniform cell spreads in space, which in turn increases the probabilities for cells to acquire nutrients; therefore random walks are likely to be a positive contribution to the overall cell growth on scaffolds.