A recently developed extension to a three-dimensional finite-element Schrödinger equation solver in the total angular momentum representation was used to calculate the energy-level spectrum and wave functions for antiprotonic helium system. The accuracy of the numerical method was analyzed. Relativistic and QED corrections to the energy levels were calculated in the main order. Excellent agreement was reached between relativistically corrected wavelengths and recent experimental data. Radiative transition probabilities and lifetimes were calculated and compared with other calculations as well as with experiment.