We demonstrate the growth of isolated InAs quantum dots on the sidewalls of core-shell GaAs/InP nanowires based on the vapor-liquid-solid MOCVD method. The quantum dots are grown under the Stranski-Krastanov mode and exhibit defect-free zinc blende structure. Discrete sharp emission peaks are observed in the range of 1.37-1.39 eV, with linewidths ranging from several hundred mu eV to 1 meV or more. Excitonic and biexcitonic emissions are observed, exhibiting different power-dependent intensity and linewidth behavior. This work may open a way for the fabrication of single photon devices based on the vapor-liquid-solid MOCVD method.