Crystal anisotropy provides a powerful route for realizing direction-dependent transport in solid-state systems. While its influence on electronic transport is well established, the role of anisotropy in magnon spin transport in van der Waals magnets is largely unexplored. Here, in a nonlocal geometry, utilizing the monoclinic van der Waals antiferromagnet CrPS₄, we observe pronounced anisotropy in both electrically and in thermally excited magnon spin transport. Electrically generated magnons exhibit a magnon spin conductivity at least 2.2 times larger and a spin diffusion length at least 2.7 times longer for transport along the crystallographic-b axis compared to the crystallographic-a axis, where λₘᵃ ∼ 211 nm and λₘᵇ ≥ 575 nm. In comparison, at 8T, we find the nonlocal second-harmonic resistance associated with thermally excited magnons to be ∼7 times larger along the crystallographic-b axis at 25K. We further show that a magnon spin diffusion length cannot be reliably extracted from the nonlocal second-harmonic resistance, owing to the extended temperature profile within CrPS₄. Likewise, we show that the anisotropy in the spin Seebeck coefficients cannot be reliably estimated from the thermally excited magnon spin transport alone, as it is intertwined with the anisotropic heat conductivity of CrPS₄. Utilizing the electrically generated magnon spin transport, we demonstrate that intrinsic crystalline anisotropy serves as an effective control parameter for tuning magnon spin transport, opening new avenues for magnonic device engineering.