Channel feedback is essential for frequency division duplex (FDD) massive multiple-input multiple-output (MIMO) systems to realize precoding and power allocation. Traditional codebooks for channel feedback, where the required number of feedback bits is proportional to the number of base station (BS) antennas, can not scale up with massive MIMO due to the large number of BS antennas. To solve this problem, in this paper, we propose an angle-of-departure (AoD) adaptive subspace codebook to reduce the codebook size and feedback overhead. Specifically, by leveraging the concept of angle coherence time, which implies that the path AoDs vary much slower than path gains, we propose an AoD-adaptive subspace codebook to quantize the channel vector in a more accurate way. We also provide performance analysis of the proposed AoD-adaptive subspace codebook, where we prove that the required number of feedback bits only scales linearly with the number of resolvable AoDs, which is much smaller than the number of BS antennas. This quantitative result is also verified by simulations.