We propose a highly-efficient broadband up-conversion technique， which enables the efficient production of broadband 2.5th harmonic lasers （centered at 421.5 nm） in the violet-blue region from fundamental Nd∶glass lasers （at 1 054 nm）. Based on the nonlinear mixing of a frequency-doubled Nd：glass laser and a broadband mid-infrared laser centered at 2 100 nm with an incident energy ratio of 4∶1， and a noncollinear configuration that enables simultaneous phase-matching and group-velocity matching， a broadband 2.5^th harmonic laser with a pulsed energy of 12.4 J and a bandwidth of 10.4 nm （relative bandwidth bigger than 2%） is produced. These results indicate the potentiality of producing high-power violet-blue lasers in 100-TW scale， and provide guidelines for developing ultrashort ultraintense lasers at short-wavelengths.