Extending the spectral wavelengths of the diode-pumped Nd-doped lasers at 1.3 μm with the KTP crystal in the intracavity Raman configuration is reported for the first time to the best of our knowledge. A systematic comparison is performed to show that a better optical conversion efficiency for the Nd:YAP/KTP Raman laser could be achieved thanks to the higher peak power and linearly polarized radiation at 1341 nm, whereas up to four Stokes emission lines are generated from the Nd:YAG/KTP Raman laser as a result of the fundamental dual-color operation at 1319 and 1338 nm. The maximum Stokes output power of the developed Nd:YAP/KTP Raman laser reaches 1.04 W under an incident pump power of 16 W and a pulse repetition rate of 10 kHz, corresponding to the diode-to-Stokes conversion efficiency as high as 6.5%. The largest pulse energy and highest peak power are evaluated to be up to 104 μJ and 34.7 kW, respectively.