In this research, the new distribution is being built depending on the Rayleigh - Weibull distribution which is called a new transmuted Rayleigh - Weibull distribution (TRWD). The distribution was built by adding the conversion parameter ß, | ß | ≤1. At first, the probability cumulative function and the possibility density function and hazard function and survival function were found by relying on the transformation rules, and the statistical characteristics of (TRWD) encompass median, mean, and moments of the origin. Consequence of studying the moments of the origin, found the difference and the first mean, skewness, kurtosis, also it will be found characteristics function, factorial generating function, mean time to failure, quantile function and the median. In addition to this, provide each of Renyi entropy measure and the order statistic property. The parameters of (TRWD) estimate by maximum probability assessment method, and hence of comparing the (TRWD) with other distributions by utilizing some statistical criteria for example the AIC, Hannan–Quinn criterion (HQIC), AICC, and BIC. The findings show us that new distribution is more flexible than continuous distributions compared to it because the value of the criteria for the (TRWD) is lower than other distributions.