Two parameters Maxwell–Exponential distribution was proposed using the Maxwell generalized family of distribution. The probability density function, cumulative distribution function, survival function, hazard function, quantile function, and statistical properties of the proposed distribution are discussed. The parameters of the proposed distribution have been estimated using the maximum likelihood estimation method. The potentiality of the estimators was shown using a simulation study. The overall assessment of the performance of Maxwell-Exponential distribution was determined by using two real-life datasets. Our findings reveal that the Maxwell–Exponential distribution is more flexible compared to other competing distributions as it has the least value of information criteria.