Current-status data arise when an event time is observed only through an indicator of whether it occurred before an examination time. This paper studies a nonparametric neural-network sieve maximum likelihood estimator of the conditional cumulative distribution function of the event time. Under Hölder smoothness assumptions, we establish an explicit convergence rate by combining approximation theory for rectified linear unit neural networks with empirical-process arguments. This result provides theoretical support for neural-network estimation and subsequent inference under current-status observation.