Massive multi-input multi-output (MIMO) in Frequency Division Duplex (FDD) mode suffers from heavy feedback overhead for Channel State Information (CSI). In this paper, a novel manifold learning-based CSI feedback framework (MLCF) is proposed to reduce the feedback and improve the spectral efficiency for FDD massive MIMO. Manifold learning (ML) is an effective method for dimensionality reduction. However, most ML algorithms focus only on data compression, and lack the corresponding recovery methods. Moreover, the computational complexity is high when dealing with incremental data. Considering to utilize the intrinsic manifold structure where the CSI samples reside, we propose a landmark selection algorithm to describe the topological skeleton of this manifold. Based on the learned skeleton, the local patch of the incremental CSI on the manifold can be easily determined by its nearest landmarks. This motivates us to propose an incremental CSI compression and reconstruction scheme by keeping the local geometric relationships with landmarks invariant. We theoretically prove the convergence of the proposed landmark selection algorithm. Meanwhile, the upper bound on the error of approximating CSI with landmarks is derived. Simulation results under an industrial channel model of 3GPP demonstrate that the proposed MLCF outperforms existing deep learning based algorithms.