This article aims to study the quantitative eddy current testing of structures of carbon fiber reinforced polymer (CFRP) material; numerical schemes for forward and inverse analysis of eddy current testing signals are proposed and validated for eddy current testing of the CFRP material. At first, an efficient forward solver based on the database approach is updated to treat anisotropic eddy current problem for efficient simulation of the eddy current testing signals due to crack in CFRP material, and an inversion scheme based on the conjugate gradient method is developed using the updated fast forward solver for sizing defect in a CFRP plate. Second, a hybrid inverse analysis scheme is proposed and implemented to improve the sizing accuracy of crack in a CFRP plate using eddy current testing signals of high frequency. Third, eddy current testing signals due to artificial cracks in a CFRP plate are measured and adopted to reconstruct the profile of the cracks. A good agreement between the true and the reconstructed defect sizes demonstrated the validity of both the fast forward solver and the new inversion scheme for sizing defects in the CFRP plate from eddy current testing signals.