Van der Waals (vdW) materials exhibit optical anisotropy due to the fundamental difference between in-plane (IP) covalent bonds and out-of-plane (OP) vdW bonds. In particular, InSe, a vdW material, provides an excellent platform for studying the optical properties of anisotropic excitons. We measure the energy difference between excitons with IP and OP dipole responses in InSe to be 0.4 meV. Under photoexcitation with femtosecond pulses, the photocarriers screen the excitons and can increase the energy difference between IP and OP optical responses to as much as 8 meV. This energy difference results from the varying screening lengths along the IP and OP directions. The change in energy difference persists for over 100 ps at 77 K, but recovers much faster, within 100 ps, at room temperature. The dependence of carrier density on the anisotropic screening of excitons has also been investigated.