Theoretical analysis of a reaction-diffusion process involved in packed bed photobioreactor with immobilized-cell is presented. Good approximate analytical expressions for the non-linear reaction-diffusion equations for substrate and product concentrations are derived. Modified Adomian decomposition method is used to derive the dimensionless concentration under steady-state condition. To see the efficiency, our analytical results are compared with the numerical results. For all different concentrations, the analytical results matched well with the simulated results. The close matching of simulated and the analytical data shows that our proposed solution is able to simulate the dynamic performance of system using the parameters. © 2015 Elsevier B.V.All rights reserved.