α‐Phase molybdenum trioxide(α‐MoO3) is a biaxial van der Waals semiconductor that can naturally support anisotropic phonon polaritons with elliptic and hyperbolic in‐plane dispersion. α‐MoO3 can meet critical coupling (CC) condition for both transverse magnetic (TM) and transverse electric (TE) polarizations along the x and y directions and exhibit high absorption in the mid‐infrared region due to strong phonon polaritons. In this study, an absorber composed of few‐layer α‐MoO3 and one‐dimensional photonic crystal separated by a cavity is proposed. Perfect absorption for TE and TM polarized light is achieved at the longitudinal and transverse optical phonon frequencies, respectively. The underlying mechanism of perfect absorption is investigated by using coupled mode theory and simulating electric field and power dissipation profiles. The results prove that CC is responsible for the perfect absorption. Moreover, the influence of the thickness of α‐MoO3 layer, width of cavity between α‐MoO3 and photonic crystal, and angle of incident light on the CC and absorption performance are examined. Accordingly, the rules for realizing perfect absorption at different operation frequencies are established. Overall, this study provides useful insights on designing a perfect absorber based on α‐MoO3 for detection and sensing applications in the mid‐infrared region.