Herein, we present a theoretical study of how Fermi-surface distortion affects symmetric nuclear matter, pure neutron matter, and neutron-star matter. The results indicate that, for the binding energy of symmetric nuclear matter, the generally accepted value extracted from the Bethe-Weizäcker mass formula for nuclei can constrain the degree of anisotropy because of Fermi-surface deformation δ 0.05. The value of δ starts to affect the stiffness of the equation of state for symmetric nuclear matter and pure neutron matter when δ 0.01. Moreover, if the Fermi surface is distorted, the results indicate that neutron stars can be deformed into an oblate shape. This deformation depends on two factors: the stiffness of the corresponding equation of state and value of δ. The corresponding deformation near the maximum neutron-star mass comes from the anisotropic pressure within these stars, which is caused by the distortion of Fermi surface predicted by the equation of state of the models.