Software reliability has become an increasingly important characteristic as software systems continue to be integrated into all parts of our lives. While the occurrence of failure after a period of time is within the nature of all software systems, the ability to estimate and predict failure is greatly beneficial to software development and maintenance. Hence, Software Reliability Growth Models (SRGMs) were developed to fulfill this requirement. Conventional parameter estimation methods of SRGM functions were complex and left more to be desired. Consequently, metaheuristics such as Swarm Intelligence algorithms were introduced to estimate and optimize the parameters of SRGM functions. Likewise, Swarm Intelligence algorithms were found to be exceptionally effective in estimating and optimizing the parameters of SRGM functions. This paper presents a novel approach to parameter estimation on three different SRGM functions through Harris’ Hawks Optimization (HHO). The proposed HHO design is compared against numerous different variants of Swarm Intelligence algorithms and is shown to be significantly more efficient than the majority of the compared designs. Moreover, as the proposed design is a base variant of Swarm Intelligence algorithms, various avenues of future improvements have also been presented to improve its overall prediction accuracy.