Interval-censored data often arise naturally in medical, biological, and demographical studies. As a matter of routine, the Cox proportional hazards regression is employed to fit such censored data. The related work in the framework of additive hazards regression, which is always considered as a promising alternative, remains to be investigated. We propose a sieve maximum likelihood method for estimating regression parameters in the additive hazards regression with case II interval-censored data, which consists of right-, left- and interval-censored observations. We establish the consistency and the asymptotic normality of the proposed estimator and show that it attains the semiparametric efficiency bound. The finite-sample performance of the proposed method is assessed via comprehensive simulation studies, which is further illustrated by a real clinical example for patients with hemophilia.