Durability of steel reinforced concrete (RC) structures is a growing problem of the civil engineering profession in the recent years. Corrosion of steel reinforcement is one of the main causes of poor durability. Accurately predicting the corrosion rates in concrete is a very challenging problem as it is affected by various factors such as the porosity and tortuosity of the concrete, the pH of the pore solution, electrical connectivity of the steel reinforcement, and electrical resistivity of concrete among others. Corrosion of the steel reinforcement is classified into two main categories as micro-cell corrosion and macro-cell corrosion, while the surface of the steel reinforcement is classified as an active surface or a passive surface. The steel surface initially has a passive layer due to high pH of the concrete pore solution. Once the chloride ions near the steel surface exceed a threshold limit, the passive layer of reinforcement deteriorates and converts into an active surface. Conversion of the passive layer into an active layer, and the existence of micro-cell and macro-cell corrosion makes it difficult to predict the corrosion rate of the steel reinforcement. In this study, an algorithm that can predict the time-varying corrosion rate of the steel reinforcement is developed and implemented in the Multiphysics Object-Oriented Simulation Environment (MOOSE) developed by the U.S. Idaho National Laboratory. The effects of environmental conditions such as temperature and humidity during curing and exposure period on the ensuing concrete properties, the surface chloride concentration and the pH of the pore solution are considered in the simulations. The results are first validation using data from literature on corrosion rate measurements. Then the validated model is applied to a RC beam as a case study to study the time-varying corrosion process.