As the increasing requirement of channel capacity for next-generation mobile broadband communication systems, three-dimensional multiple-input multiple-output (3D MIMO) systems have been attracting much attentions in recent years. Accurate channel estimation is inevitably one of the most essential tasks for designing the 3D MIMO systems. This paper first studies the sparsity of 3D MIMO channel and then proposes a sparse channel estimation method based on Quantum Bacterial Foraging Optimization (QBFO) algorithm. Numerical simulations are conducted to confirm that the proposed algorithm can greatly improve estimation performance compared to traditional estimation algorithms.