A new sole parameter probability distribution named the Tornumonkpe distribution has been derived in this paper. The new model is a blend of gamma (2, and gamma(3 distributions. The shape of its density for different values of the parameter has been shown. The mathematical expression for the moment generating function, the first three raw moments, the second and third moments about the mean, the distribution of order statistics, coefficient of variation and coefficient of skewness has been given. The parameter of the new distribution was estimated using the method of maximum likelihood. The goodness of fit of the Tornumonkpe distribution was established by fitting the distribution to three real life data sets. Using -2lnL, Bayesian Information Criterion (BIC), and Akaike Information Criterion(AIC) as criterial for selecting the best fitting model, it was revealed that the new distribution outperforms the one parameter exponential, Shanker and Amarendra distributions for the data sets used.