Hybrid massive arrays have been widely used in direction of arrival (DOA) estimation for it can provide larger aperture with lower hardware complexity. However, as the signals received by a hybrid array are compressed by the phase shifter network or the switch network, the degree of freedom (DOF) or spatial resolution of hybrid array is lower than fully-digital (FD) array with same number of antennas. Therefore, we develop a novel sparse hybrid array called switches-based sparse hybrid array (SW-SHA) which by combining nested array and switches-based hybrid array to achieve a huge improvement on DOF over traditional hybrid arrays. Simulations of the spatial spectrums verify that SW-SHA can accurately solve the problem of DOA estimation with the number of signal sources much larger than the number of RF chains. Finally, to further improve the accuracy of DOA estimation for SW-SHA, MMV-SW-SHA is proposed by transforming the single-snapshot co-array signal into MMV form. The simulation results also show that MMV-SW-SHA has better performance than SW-SHA when signal-to-noise ratio (SNR) is low.