We present the first observation, to the best of our knowledge, the spontaneous generation of picoseconds pulse trains in a diode-pumped Nd:YAP laser with gigahertz repetition rate. Spatially dependent temporal dynamics were experimentally observed. After theoretically reconstruct the experimental temporal-resolved patterns, we verify that the complicated spatially-dependent temporal dynamics were originated from simultaneous coherent locking combination of fundamental and several additional higher-order transverse modes.