The quantum defect (QD) is an important issue that demands prompt attention in high-power fiber lasers. A large QD may aggravate the thermal load in the laser, which would impact the frequency, amplitude noise and mode stability, and threaten the security of the high-power laser system. Here, we propose and demonstrate a cladding-pumped Raman fiber laser (RFL) with QD of less than 1%. Using the Raman gain of the boson peak in a phosphorus-doped fiber to enable the cladding pump, the QD is reduced to as low as 0.78% with a 23.7 W output power. To our knowledge, this is the lowest QD ever reported in a cladding-pumped RFL. Furthermore, the output power can be scaled to 47.7 W with a QD of 1.29%. This work not only offers a preliminary platform for the realization of high-power low-QD fiber lasers, but also proves the great potential of low-QD fiber lasers in power scaling.