In this paper, we introduced a new flexible extension of the Generalized Half Normal lifetime model as well as a new log-location regression model based on the proposed model. Some useful characterization results are presented and some mathematical properties are derived. The maximum likelihood method is used to estimate the model parameters by means of a graphical Monte Carlo simulation study. We show that the new log-location regression lifetime model can be very useful in analysing real data and provide more realistic fits than other regression models. Index plot of the modified deviance residual and Q-Q plot for modified deviance residual are presented to illustrate that our new model is more appropriate to HIV data set than other competitive models like log-odd log-logistic generalized half-normal regression model and log-generalized half-normal regression model. The sensitivity analysis is used via the index plot of generalized cook distance to discover the possible influential observations.