We study a tunable-focus lens with convex and flat electrodes in a homogeneous liquid crystal (LC) cell. In a voltage-on state, a centro-symmetric gradient refractive index is generated within the LC layer, which causes the focusing behavior for the extraordinary wave. There have been experimental studies of the systems with spherical or parabolic shape of the top electrodes and there is a need in the theoretical modeling. We present a theoretical model of the lens with spherical top electrode and analyze its properties. We solve the Maxwell equations that are coupled to the Euler-Lagrange equations from the variational principle applied to the total free energy minimization. LC director spatial profile is found subject to the applied voltage. After that the phase retardation profile of the test light beam is calculated and thus a focal length dependence on the applied field. The simulation results agree well with experimental data. This LC lens has advantages in relatively large focal length range and low operating voltage.