In this research, we will introduce a new distribution, which is called the new exponentiated exponential-Rayleigh distribution, which is built by adding the shape parameter to the cumulative function of the exponential-Rayleigh distribution resulting from merging the cdf function of three parameters continuous distribution. Two of these parameters are scale parameters, and another is the shape parameter and this is to make this new continuous statistical distribution more flexible than other continuous statistical distributions. Besides, discuss the mathematical and statistical properties of this new distribution, including (the mode, the median, the moments about the origin, the coefficients of skewness and kurtosis, the characteristic function, the moment-generating function, the factorial moments-generating function, and the mean time to failure). The shape property of each of the pdf, cdf, and hazard functions was also studied. Multiple shapes were drawn with different parameter values ​​for each of the PDF, CDF, survival, and hazard functions. An organisational table was also created for some of these properties