Quasi-Z-source inverter (QZSI) can boost and buck the input voltage with only once power transformation. It is suitable for the grid-connected photovoltaic (PV) system with the wide variation of PV cell output. The composite control for PV grid-connected and energy-storage based on Quasi-Z-source inverter is researched in this paper. The energy balance between the pre-stage circuit and the post-stage circuit is achieved automatically by using the storage battery. In the grid-connected photovoltaic system based on Quasi-Z-source inverter with energy-storage device, the fluctuant peak of DC-link voltage is caused by the change of maximum power point for photovoltaic cell, and the grid-connected current is perturbed. Faced with these problems, the strategy of the variable-parameter PI control of the grid-connected current is proposed in this paper. The PI parameters of the grid-connected current are adjusted according to the fluctuant peak of DC-link voltage. When using the variable-parameter PI control method, the perturbation to the grid-connected current is smaller than that of the traditional method. When the voltage is changed at the maximum power point for photovoltaic cell, THD of the grid-connected current is reduced effectively.