We propose a technique to modulate the pump light of phase-shift pulse Brillouin optical time domain analysis (PSP-BOTDA) with Walsh code in a nested configuration. We call it dual Walsh codes PSP-BOTDA. In this technique, two Walsh codes are each assigned to return-to-zero (RZ) and non-return-to-zero (NRZ) pulses. Simulation and experiment results have shown that the assignment of Walsh to the non-return-to-zero (NRZ) pulses even for code duration of longer than the time constant of the acoustic wave still attains the theoretical spatial resolution of the Brillouin signal, in contrast to that of previously proposed dual Golay codes PSP-BOTDA. In terms of the optical signal-to-noise ratio (SNR), we obtained a maximum of improvement of 5.4 dB, compared to the conventional technique.