Pair-density-wave (PDW) superconductivity is a state in which the superconducting order parameter modulates at a finite wavevector. Using large-scale density matrix renormalization group, we study the doped altermagnetic Mott insulator in the checkerboard t-J model, where altermagnetic exchange anisotropy is encoded microscopically through anisotropic ferromagnetic next-nearest-neighbor exchange. By mapping the ground-state phase diagram as a function of doping and altermagnetic anisotropy, mainly on six-leg cylinders, we identify a transition from a uniform d-wave superconducting regime with charge modulation to a PDW regime coexisting with stripe order. In the PDW regime, we report an unconventional wave-vector locking Q_PDW≈ 2Q_Stripe along the cylinder direction, in contrast to the conventional relation. Pair correlations reveal a two-scale structure, consisting of short-distance local d-wave pairing and long-distance finite-momentum PDW correlations. A symmetry-based Ginzburg–Landau analysis is presented for the observed locking. Our results identify altermagnetism as a strong-coupling, microscopically grounded route to finite-momentum superconductivity in doped Mott insulators.