In a case-cohort design, covariate histories are measured only on cases and a subcohort that is randomly selected from the entire cohort. This design has been widely used in large epidemiologic studies, especially when the exposures of interest are expensive to assemble for all the subjects. In this paper, we propose statistical procedures for analyzing case-cohort sampled current status data under the additive hazards model. Asymptotical properties of the proposed estimator are described and we suggest a resampling method to estimate the variances. Simulation studies show that the proposed method works well for finite sample sizes, and one data set is analyzed for illustrative purposes.