We study the structure of relativistic stars in R+αR^2 theory using the method of matched asymptotic expansion to handle the higher order derivatives in field equations arising from the higher order curvature term. We find solutions, parametrized by α, for uniform density stars. We obtain the mass-radius relations and study the dependence of maximum mass on α. We find that M_ is almost linearly proportional to α. For each α the maximum mass configuration has the biggest compactness parameter (η

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... = GM/Rc^2), and we argue that the general relativistic stellar configuration corresponding to α=0 is the least compact among these.