A new shared frailty model for recurrent gap time data is introduced, assuming that frailty acts additively on a Weibull rate function derived from a non-homogeneous Poisson process. The frailty is included with two purposes: to handle within-subject correlation and to accommodate zero-recurrence subjects. With this intention, we assume that the frailty has a non-central chi-squared distribution with zero degrees of freedom. The proposed model has two special cases without frailty, namely the Weibull rate model and the classical homogeneous Poisson process. Furthermore, since the model is fully specified, the maximum likelihood method is applied for parameters estimation based on a marginal likelihood function. Particular attention is devoted to the likelihood construction for bivariate recurrent event data. An application to a well-known data set is provided to elucidate the practical contribution of the new survival model.