This paper proposes a technique for estimating the computational time of programs in an actor model, which is intended to serve as a compiler target of a wide variety of actor-based programming languages. We define a compositional translation function returning cost equations, which are fed to an automatic off-the-shelf solver for obtaining the time bounds. Our approach is based on a new notion of synchronization sets, which captures possible difficult synchronization patterns between actors and helps make the analysis efficient and precise. The approach is proven to correctly over-approximate the worst computational time of an actor model of concurrent programs. Our technique is complemented by a prototype analyzer that returns upper bound of costs for the actor model.