In the present paper we investigate the structure of relativistic stars in 4D Einstein-Gauss-Bonnet gravity .
The mass-radius relations are obtained for realistic hadronic and for strange quark star equations of state , and for a wide range of the Gauss-Bonnet coupling parameter \alpha .
Even though the deviations from general relativity for nonzero values of \alpha can be large enough , they are still comparable with the variations due to different modern realistic equations of state if we restrict ourselves to moderate value of \alpha .
That is why the current observations of the neutron star masses and radii alone can not impose stringent constraints on the value of the parameter \alpha .
Nevertheless some rough constraints on \alpha can be put .
The existence of stable stellar mass black holes imposes \sqrt { \alpha } \lesssim 2.6 { km } for \alpha > 0 while the requirement that the maximum neutron star mass should be greater than two solar masses gives \sqrt { | \alpha| } \lesssim 3.9 { km } for \alpha < 0 .
We also present an exact solution describing the structure of relativistic stars with uniform energy density in 4D Einstein-Gauss-Bonnet gravity .