  We propose a systematic scheme to engineer quantum states of a quantum system
governed by a time-convolutionless non-Markovian master equation. According to
the idea of reverse engineering, the general algebraic equation to determine
the control parameters, such as coherent and incoherent control fields, is
presented. Without artificially engineering the time-dependent decay rates and
retaining the environment-induced Lamb shifts, the quantum state can still be
transferred into the target state in a finite period of time along an arbitrary
designed trajectory strictly in Hilbert space. As an application, we apply our
scheme to a driven two-level non-Markovian system and realize
instantaneous-steady-state tracking and a complete population inversion with
control parameters which are available in experimental settings.
