We develop a novel method of measuring the lensing distortion profiles of clusters with stacking the ``scaled'' amplitudes of background galaxy ellipticities as a function of the ``scaled¡Ç' centric radius according to the Navarro-Frenk-White (NFW) prediction of each cluster, based on the assumption that the different clusters in a sample follow the universal NFW profile. We apply this method to the Subaru weak lensing data and the {\it XMM}/{\it Chandra} X-ray observables for a sample of 50 massive clusters in the redshift range 0.15< z< 0.3$, where their halo masses range over an order of magnitude. To estimate the NFW parameters of each cluster, we use the halo mass proxy relation of X-ray observables, based on either the hydrostatic equilibrium or the gas mass, and then infer the halo concentration from the model scaling relation of halo concentration with halo mass. We evaluate a performance of the NFW scaling analysis by measuring the scatters of 50 cluster lensing profiles relative to the NFW predictions over a range of radii, 0.14