We demonstrate a dual-operation-mode liquid crystal (LC) lens, which is fabricated with the silica nanoparticle-doped (SND) hybrid-aligned nematic (HAN) LC cell. With AC voltage, the cell behaves as a conventional LC lens. The response time of the SND HAN LC lens is faster than that of the conventional LC lens, which is fabricated using the pristine HAN LC cell. This is because that the doped silica nanoparticles may decrease the dielectric relaxation time constant of the cell. The addition of the silica nanoparticles also increases the viscosity of the LC host, suppresses the backflow motion of the LCs and then decreases the response time of the SND LC lens. With DC voltage, the electrophoretic motion of the doped silica nanoparticles and the agglomerate silica networks on the substrate surface cause the SND HAN LC cell to function as a bistable LC lens.