A novel approach is proposed to design a devoted subspace codebook for the equivalent channel feedback in lens-based millimeter-wave (mmWave) massive MIMO systems. The equivalent channel state information (CSI) between users and radio frequency RF chains required at the base station (BS) to achieve multi-user (MU) multiplexing gain. There is no such codebook designed for the channel feedback for such emerging lens-based mmWave massive multiple-input multiple-output (MIMO) system with low channel feedback overhead. For such a purpose, I propose the subspace codebook with reduced-dimension, which can substantially decrease the codebook size, RF chains and channel feedback overhead. Particularly, I first generate the high-dimensional channel vectors in the channel subspace by utilizing the limited scattering property of the mmWave channels. After this, the equivalent channel vector (ECV) is quantized by proposing the dimension-reduced subspace codebook which utilizes the function of lens and beam selector respectively. Simulation results revealed that the proposed codebook for channel feedback performs was much better than the classical channel codebook.