We study the branching ratios of the radiative leptonic B-c decays of B-c(+)-->l(+) nu(l)gamma (l=e,mu,tau). In our analysis, the form factors for B-c-->gamma transitions are calculated directly in the entire physical range of momentum transfer within the light front framework. We find that the decay branching ratios of B-c(+)-->e(+)nu(e)gamma, B-c(+)-->mu(+) nu(mu)gamma, and B-c(+)-->tau(+) nu(tau)gamma are 2.0X10(-5), 2.3X10(-5), and (8.8-10.7)X10(-5), compared with 1.3X10(-9), 5.6X10(-5), and 1.4X10(-2) for that of B-c(+)-->e(+)v(e), B-c(+)-->mu(+)nu(mu), and B-c(+)-->tau(+)nu(tau), respectively. [S0556-2821(99)08209-0].