On the basis of White's theory, an improved renormalization group (RG) theory is developed for chain bonding fluids inside the critical region. Outside the critical region, the statistical associating fluid theory based on the first-order mean sphere approximation [Fluid Phase Equilibria 171, 27 (2000)] is adopted and all the microscopic parameters are taken directly from its earlier application of real fluids. Inside the critical region, the RG transformation for long-range density fluctuation is derived in the k space, which illustrates explicitly the contributions from the mean-field term, the local density fluctuation, and the nonlocal density fluctuation. The RG theory is applied to describe physical behavior of ten n alkanes (C1-C10) both near to and far from the critical point. With no additional parameters for chain bonding fluids, good results are obtained for critical specific heat and phase coexistence curves and the resulting critical exponents are in good agreement with the reported nonclassic values.