In this paper, we propose an effective approach to estimate the parameters of software reliability growth model (SRGM) using a real-valued genetic algorithm (RGA). The existing SRGMs require the estimation of the parameters such as the total number of failures or the failure detection rate using numerical methods, maximum likelihood estimation or least square estimation. However, these methods impose certain constraints on the parameter estimation of SRGM like requiring the continuity and existence of derivatives in the modelling function. RGA is free from the constraints on the parameter estimation of SRGM. Moreover, it is more adapted in optimization of continuous domain such as parameter estimation of SRGM than a binary genetic algorithm. Two real-valued genetic operators, heuristic crossover and non-uniform mutation, are applied to improve the accuracy and performance of the parameter estimation of SRGM. We conducted experiments on eight real world datasets for comparing the proposed approach with the numerical methods and other existing genetic algorithms. The results indicate that the RGA is more effective in the parameter estimation of SRGM than other GA approaches. We believe that RGA can be a promising solution to effectively managing software quality through the accurate reliability estimates.