The Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) is the well-known combinatorial optimization problem having numerous valuable applications in operations research. Unlike the classic CVRP (without time windows constraints), approximability of the CVRPTW (even in the Euclidean plane) in the class of algorithms with theoretical guarantees is much less studied. To the best of our knowledge, the family of such algorithms is exhausted by the Quasi-Polynomial Time Approximation Scheme (QPTAS) proposed by L. Song et al. for the general setting of the planar CVRPTW and two our recent approximation algorithms, which are Efficient Polynomial Time Approximation Schemes (EPTAS) for any fixed capacity q and number p of time windows and remain PTAS for slow-growing dependencies \(q=q(n)\) and \(p=p(n)\). In this paper, combining the well-known instance decomposition framework by A. Adamaszek et al. and QPTAS by L. Song et al. we propose a novel approximation scheme for the planar CVRPTW, whose running time remains polynomial for the significantly wider range of q and p.