The Capacitated Vehicle Routing Problem (CVRP) is the well-known combinatorial optimization problem having a wide range of practical applications in operations research. It is known that the problem is NP-hard and remains intractable even in the Euclidean plane. Although the problem is hardly approximable in the general case, some of its geometric settings can be approximated efficiently. Unlike other versions of CVRP, approximability of the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) by the algorithms with performance guarantees seems to be weakly studied so far. To the best of our knowledge, the recent Quasi-Polynomial Time Approximation Scheme (QPTAS) proposed by L. Song et al. appears to be the only one known result in this field. In this paper, we propose the first Efficient Polynomial Time Approximation Scheme (EPTAS) for CVRPTW extending the classic approach of M. Haimovich and A. Rinnooy Kan.