The violet-green laser converter based on a molecular-beamepitaxy (MBE) grown CdSe quantum dot (QD) laser heterostructure pumped by a commercial InGaN laser diode (LD) emission has been fabricated and studied in detail. The optimized II-VI laser heterostructure consists of asymmetrical ZnSe/ZnSSe superlattice (SL) waveguide and active region comprising five CdSe QD sheets (QDS) placed in the centre of 2-nm-thick ZnSe quantum wells. The new laser structure design provides both a high homogeneity of optical pumping of the CdSe QDS due to tunnelling of charge carriers between the QDS separated by 5-nm-thick ZnSe/ZnSSe/ZnSe barriers and high optical confinement factor. Optimization of both cavity length of the II-VI laser and parameters of optical focusing system to obtain a narrow stripe with the length slightly exceeding the cavity length has been performed. As a result, the maximum achieved quantum efficiency and pulse output power in green have been as high as 8% and 65 mW, respectively.