We propose a new extended regression model based on the logarithm of the generalized odd log-logistic Weibull distribution with four systematic components for the analysis of survival data. This regression model can be very useful and could give more realistic fits than other special regression models. We obtain the maximum likelihood estimates of the model parameters for censored data and address influence diagnostics and residual analysis. We prove empirically the importance of the proposed regression by means of a real data set (survival times of the captive snakes) from a study carried out at the Herpetology Laboratory of the Butantan Institute in São Paulo, Brazil.