We present a new determination of the concentration-mass relation for galaxy clusters based on our comprehensive lensing analysis of 19 X-ray selected galaxy clusters from the Cluster Lensing and Supernova Survey with Hubble ( CLASH ) . Our sample spans a redshift range between 0.19 and 0.89 . We combine weak-lensing constraints from the Hubble Space Telescope ( HST ) and from ground-based wide-field data with strong lensing constraints from HST . The result are reconstructions of the surface-mass density for all CLASH clusters on multi-scale grids . Our derivation of NFW parameters yields virial masses between 0.53 \times 10 ^ { 15 } M _ { \odot } / h and 1.76 \times 10 ^ { 15 } M _ { \odot } / h and the halo concentrations are distributed around c _ { 200 \textrm { c } } \sim 3.7 with a 1 \sigma significant negative trend with cluster mass . We find an excellent 4 % agreement between our measured concentrations and the expectation from numerical simulations after accounting for the CLASH selection function based on X-ray morphology . The simulations are analyzed in 2D to account for possible biases in the lensing reconstructions due to projection effects . The theoretical concentration-mass ( c-M ) relation from our X-ray selected set of simulated clusters and the c-M relation derived directly from the CLASH data agree at the 90 % confidence level .