Natural gas hydrate is a new type of green energy resources and has great development prospects, and it has attracted worldwide attentions. The exploitation of natural gas hydrate may result in a series of geological disasters. Therefore, the constitutive model of natural gas hydrate bearing sediments needs to be established to reveal deformation laws of the reservoir sediments and accurately evaluate mechanical properties of hydrate reservoirs. This is the basic guarantees for the effective exploitation of natural gas hydrate resources. The triaxial compressive tests were conducted on samples of natural gas hydrate sediment. Furthermore, the Duncan-Chang hyperbolic model was modified by considering the influences of hydrate saturation based on the test results to obtain the constitutive model according with the deformation characteristics of natural gas hydrate reservoirs. The results show that the stress-strain curves of natural gas hydrate reservoirs show unobvious compaction stage and peak strength, short elastic stage, long yield stage, and significant strain hardening characteristics. After applying loads on natural gas hydrate bearing sediments, the internal solid particles were dislocated and slid. When the loads were small, the sediments demonstrated elastic deformation. With the increase of loads, plastic flows appeared in the interior, and the hydrate crystals were re-orientated, thus the sediments showing plastic deformation. Initial tangent elastic modulus increased with the effective confining pressures, which had little correlations with hydrate saturation. Furthermore, the damage ratio increases with the increase of effective confining pressures, while slightly decreases with the increase of natural gas hydrate saturation. The predicted results of stress-strain curves of sediments with different hydrate saturations well coincide with the results of triaxial compressive tests, indicting the feasibility and rationality of this model.