For the analysis of interval-censored data, we introduce a more comprehensive generalized accelerated hazards model. This model aims to facilitate a thorough analysis of the relationship between various risk factors and the hazard of the failure time. We propose a seive maximum likelihood estimation procedure that combines fully connected neural networks and monotonic splines. We leverage fully connected neural networks to approximate the nonparametric effects, allowing for flexible and adaptive modeling of complex relationships. Under certain regularity conditions, we obtain non-asymptotic error bound of the proposed estimator and establish the asymptotic normality of the parameter estimators. To evaluate the performance of our proposed approach, we conduct a simulation study to assess its finite sample properties. Furthermore, as a real-world application, our proposed method is applied to the Atherosclerosis Risk in Communities (ARIC) study.