Millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) with hybrid precoding is a promising technique for the future 5G wireless communications. Due to a large number of antennas but a much smaller number of radio frequency (RF) chains, estimating the high-dimensional mmWave massive MIMO channel will bring the large pilot overhead. To overcome this challenge, this paper proposes a super-resolution channel estimation scheme based on two-dimensional (2D) unitary ESPRIT algorithm. By exploiting the angular sparsity of mmWave channels, the continuously distributed angle of arrivals/departures (AoAs/AoDs) can be jointly estimated with high accuracy. Specifically, by designing the uplink training signals at both base station (BS) and mobile station (MS), we first use low pilot overhead to estimate a low-dimensional effective channel, which has the same shift-invariance of array response as the high-dimensional mmWave MIMO channel to be estimated. From the low-dimensional effective channel, the superresolution estimates of AoAs and AoDs can be jointly obtained by exploiting the 2D unitary ESPRIT channel estimation algorithm. Furthermore, the associated path gains can be acquired based on the least squares (LS) criterion. Finally, we can reconstruct the high-dimensional mmWave MIMO channel according to the obtained AoAs, AoDs, and path gains. Simulation results have confirmed that the proposed scheme is superior to conventional schemes with a much lower pilot overhead.