Predicting software vulnerabilities effectively is crucial for enhancing cybersecurity measures in an increasingly digital world. Traditional forecasting models often struggle with the complexity and dynamics of software vulnerability data, necessitating more advanced methodologies. This paper introduces a novel approach using Multi-Recurrent Neural Networks (MRN), which integrates multiple memory mechanisms and offers a balanced complexity suitable for time-series data. We compare MRNs against traditional models like ARIMA, Feedforward Multilayer Perceptrons (FFMLP), Simple Recurrent Networks (SRN), and Long Short-Term Memory (LSTM) networks. Our results demonstrate that MRNs consistently outperform these models, especially in settings with limited data or shorter forecasting horizons. MRNs show a remarkable ability to handle complex patterns and long-term dependencies more efficiently than other models, highlighting their potential for broader applications beyond cybersecurity. The findings suggest that MRNs can significantly improve the accuracy and efficiency of predictive analytics in cybersecurity, paving the way for their adoption in practical applications and further exploration in other predictive tasks.