We have demonstrated laser frequency offset locking via the Rb87 tripod-type double-dark resonances electromagnetically induced transparency (EIT) system. The influence of coupling fields' power and detuning on the tripod-type EIT profile is studied in detail. In a wide coupling field's detuning range, the narrower EIT dip has an ultranarrow linewidth of ∼590 kHz, which is about one order narrower than the natural linewidth of Rb87. Without the additional frequency stabilization of the coupling lasers, we achieve the relative frequency fluctuation of 60 kHz in a long time of ∼2000 s, which is narrower than the short-time linewidth of each individual laser.