The remarkable decadal shift of global climate in the late 1970s has been observed, as well as the decadal variability of ENSO which is the most significant coupled air-sea phenomenon in the tropical Pacific. In order to evaluate the ability of LASG/IAP (State Key Laboratory of Numerical Modeling for Armospheric Sciences and Geophysical Fluid Dynamics/Institute of Atmospheric Physics, Chinese Academy of Sciences) Climate System Ocean Model (version 1.0, abbreviated as LICOM1.0), the simulations of interannual and decadal variability of ENSO are made by the model, and the results show: LICOM could simulate the interannual variability of ENSO basically, and it is found that the ENSO feedback mechanism in the model is in agreement with theoretical investigation by calculating the surface heat content and analyzing the heat transport and the mass transport. Moreover, the model can reproduce decadal modulation of ENSO, such as period and propagation direction as well as asymmetry between the cold and warm events and their simulations are also basically near to realistic observations. And the relationship between the skewness and nonlinear dynamic heating is mainly analyzed. Further analysis also shows that there is a close relationship between the Nonlinear Dynamic Heating (NDH) and the amplitude and skewness of ENSO on the decadal timescale. It is found that there exist errors in the model simulation compared with SODA results. The model needs to be improved in the future.