Highly mode group selective photonic lanterns (PLs) are desired for mode-division multiplexing transmission systems. Usually, mode selectivity is achieved by using input fibers with different core diameters or refractive indices to break degeneracy between mode groups. We demonstrate that mode group selectivity can be greatly improved by optimizing core geometry of PLs. For three-mode PLs with optimized core geometry, based on beam propagation method (BPM) simulation results, mode selectivity is improved from 23.8 dB to 43.9 dB for LP01 mode, and mode selectivity of LP11 mode is improved from 26.8 dB to 45.5 dB. The reason is the optimized core geometry can significantly slow down the changing of mode profile along the taper of the PL; thus adiabatic tapering requirement can be greatly alleviated. It can also be observed that the simulation results by the BPM are in good agreement with calculation of coupled-mode theory.