Within the framework of Non-Relativistic Quantum Chromodynamics (NRQCD) factorization,we calculate the next-to-leading order (NLO) perturbative QCD corrections to the form factors forthe semileptonic decays of Bc* into J/ψ via (axial-)vector and (axial-)tensor currents. We obtain thecomplete analytical results for the form factors up to NLO, and provide their asymptotic expressionsin...