The COarse MEsh Transport (COMET) method, a hybrid continuous energy stochastic and deterministic transport method/tool based on the incident flux response expansion theory, is capable of providing highly accurate and efficient continuous energy whole-core neutron solutions to various heterogeneous reactor cores. In this work, a novel low-order (zeroth-order) acceleration technique is developed to significantly improve COMET’s computational efficiency for core calculations. This new method is based on consistent coupled low-order and high-order calculations to obtain the COMET core solution. In the low-order calculations, COMET is used to converge the total partial current escaping from each coarse mesh and the core eigenvalue. The resulting fixed-source problem in which the off-diagonal terms (equivalent to the scattering and fission neutron sources) are constructed by the zeroth-order solution are efficiently solved by the high-order COMET calculations. The resulting high-order angular flux on each coarse mesh bounding surface is then used to update (collapse) the low-order response coefficients. The coupled low-order and high-order calculations are repeated until both the eigenvalue and the low-order response coefficients are converged. The new acceleration method is implemented into COMET and tested in a set of stylized Advanced High Temperature Reactor (AHTR) benchmark problems. It is found that the core eigenvalues and the local fission density distributions predicted by COMET with the low-order acceleration agree very well with those computed by the original COMET. The eigenvalue discrepancy varies from 0 to 1 pcm, and the average relative differences in the stripewise and assembly-average fission density distributions are in the range of 0.021% to 0.032% and 0.004% to 0.01%, respectively. The comparisons have shown that the new low-order acceleration method can maintain COMET’s accuracy while improving its computational efficiency for core calculations by 12 to 16 times.