The two-photon state with spatial entanglement is an essential resource for testing fundamental laws of quantum mechanics and various quantum applications. Its creation typically relies on spontaneous parametric downconversion in bulky nonlinear crystals where the tunability of spatial entanglement is limited. Here, we predict that ultrathin nonlinear lithium niobate metasurfaces can generate and diversely tune spatially entangled photon pairs. The spatial properties of photons including the emission pattern, rate, and degree of spatial entanglement are analyzed theoretically with the coupled mode theory and Schmidt decomposition method. We show that by leveraging the strong angular dispersion of the metasurface, the degree of spatial entanglement quantified by the Schmidt number can be decreased or increased by changing the pump laser wavelength and a Gaussian beam size. This flexibility can facilitate diverse quantum applications of entangled photon states generated from nonlinear metasurfaces.