In order to smooth the fluctuation of photovoltaic (PV) power affected by irradiation conditions, weaken the frequent disturbance to the distribution network, and, thus, enhance its acceptance to PV, a fuel cell/supercapacitor hybrid energy storage device (FSHESS) is configured on the DC side of a grid-connected PV system, which is combined with the PV unit to form a hybrid PV power generation system, i.e., the PV-FSHESS. Based on the analysis of the electrical characteristics of the FC and the SC, an improved low-pass filtering method based on rules and considering the state of charge constraint of the SC is proposed for the power allocation of the FSHESS. With respect to the problem of DC-bus voltage stabilization, a modified variable speed integral nonlinear PI controller is presented for the purpose of overcoming the following disadvantages: (i) the ordinary PI controller cannot adaptively adjust the cumulative speed of the integral term in line with the deviation, which may cause large overshoot and oscillation; and (ii) the conventional variable speed integral controller has more parameters, which increases the difficulty of parameter tuning. The simulation verification is carried out under different operating conditions of PV output power and load demands, and the results prove the effectiveness of the proposed control scheme.