The effect of electron-electron interactions on the energy spectrum of surface electrons in a three-dimensional topological insulator is studied theoretically. The interaction includes both charge- and spin-dependent correlations. Using the Green's function method, we calculate the electron self-energy and determine the renormalized spin-orbit coupling strength. We find that the energy spectrum renormalized by spin-dependent electronic correlation turns nonlinear with respect to the wave vector k measured from the perfect Dirac cone (in the absence of electron-electron interactions). We also discuss charge screening contributions from surface and bulk electrons.