Road accidents are caused by several causative factors leading to various degrees of injury and death. This paper explored the capability of diverse machine learning algorithms in predicting the counts of road accident severity in Nigeria. Road accident data (number of accidents, causative factors, and degrees of casualty) used in this study were sourced from the National Bureau of Statistics. The correlation coefficient and analysis of variance were performed on the data. The input parameters, which were the number of accidents resulting from 18 accident causative factors, were used to predict the output parameters (minor, fatal, and serious) using different machine learning algorithms (simple linear and linear regression, random tree, support vector machine, and artificial neural network [ANN]). These algorithms were used to develop models to predict the counts by the severity (minor, fatal, and serious) of road accidents. The correlation coefficient and analysis of variance revealed that brake failure (as a mechanical factor) had the highest correlation coefficients (0.9765—fatal, 0.9842—serious, and 0.8375—minor) for the accident severity with significantly identical datasets (
p
value < 0.05). The models developed using the ANN algorithm had the highest
R
2
(92.6% for fatal, 98.7% for serious, and 89.9% for minor) for predicting the counts of accident severity, and these were associated with the lowest error values for the studied error metrics. These results showed the predictive power of the ANN algorithm to forecast the underlying nonlinear and intricate patterns inherent in the data used in this work. However, other developed machine learning models performed moderately well in predicting all the accident severities. The work demonstrated the prediction capability of the ANN algorithm in modeling accident severities and the possibility of utilizing machine learning algorithms to predict the counts of road accident severity in Nigeria.