Orthogonal time frequency space (OTFS) modulation is a two-dimensional modulation technique designed in the delay-Doppler domain, specially suitable for doubly-dispersive fading channels. In general, the conventional message passing (MP) algorithm is capable of eliminating the negative impacts of inter-symbol interferences for data detection in OTFS at the expense of high computational complexity. To reduce the receiver complexity in OTFS systems, we propose a damped generalized approximate message passing (GAMP) algorithm, where the damping factors are optimized based on deep learning (DL) techniques. Specifically, each iteration of the GAMP algorithm is unfolded into a layer-wise structure analogous to a neural network and the damping factors are learned to improve the detection performance. The optimized damping factors can be directly employed in the original GAMP algorithm without increasing its computational complexity. Simulation results demonstrate the effectiveness of the proposed algorithm and show that it can outperform the classical GAMP algorithm and the MP algorithm.