The frequency stabilization of a laser diode in the $1.3\mathrm{\mu m}$ region using double resonance optical pumping (DROP) spectrum in the $5P_{3/2}–6S_{1/2}$ transition of ${}^{87}\mathrm{Rb}$ atoms is demonstrated. The signal-to-noise ratio of the DROP spectrum is approximately ten times higher than that of the previous optical–optical double resonance spectrum. The spectral linewidth of the DROP measures $8.4\mathrm{MHz}$ . When the frequency of a $1.367\mathrm{\mu m}$ laser diode is stabilized to the DROP spectrum, the frequency stability is $9\times {10}^{-12}$ after $100\mathrm{s}$ . Also, the wavelength of the frequency-stabilized laser locked to the $5P_{3/2}–6S_{1/2}$ transition using a wavelength meter is measured.