In this study, we define the chi-square mixture of transformed gamma distribution which contained some special submodels namely, the chi-square mixture of gamma, Weibull, and exponential mixture distributions. Also, the chi-square mixture of inverse transformed gamma distribution is defined and a class of submodels are deduced, that is, the chi-square mixture of inverse gamma, inverse Weibull, and inverse exponential mixture distributions. For both classes, statistical properties are investigated, that is, mean, variance, skewness and kurtosis using rth raw moment. The limiting behavior and special cases are also given to established relationships.