We developed a metallic pressure cell made of 56Ni–40Cr–4Al (Ni–Cr–Al) alloy for use with a non-destructive pulse magnet and a magnetic susceptibility measurement apparatus with a proximity detector oscillator (PDO) in pulsed magnetic fields of up to 51 T under pressures of up to 2.1 GPa. Both the sample and sensor coil of the PDO were placed in the cell so that the magnetic signal from Ni–Cr–Al would not overlay the intrinsic magnetic susceptibility of the sample. A systematic investigation of the Joule heating originating from metallic parts of the pressure cell revealed that the increase in sample temperature is negligible at 1.4 K in magnetic fields of up to 40 T in the field-ascending process for the maximum applied magnetic field of 51 T. The effectiveness of our apparatus was demonstrated by investigating the pressure dependence of the magnetization process of the triangular-lattice antiferromagnet Ba3CoSb2O9.