There is a desperate need for extended versions of the classical distributions. There have been attempts to find novel families of probability distributions that widen existing families and provide great flexibility in data modeling in a number of application areas, including lifetime analysis, finance, and insurance. In this paper, we introduce a new family of distributions based on [0,1] Truncated and propose a new extension for the exponential distribution. The new distribution is called Truncated Nadarajah-Haghighi Distribution, symbolized with {[0,1]TNHE}. This study aims to derive some statistical properties for the new distribution, such as the quantile function, the mixture representation for the probability density function, the moments, the incomplete moments, the stress strength, the Rényi entropy, and the Shannon entropy. In addition, we estimated the parameters using the maximum likelihood method and proposed the simulation and application of the selected parameters using the statistical software R.