We report the production of 39 K and 87 Rb Bose-Einstein condensates (BECs) in the lowest hyperfine states |F = 1, mF = 1 simultaneously. We collect atoms in bright/dark magneto-optical traps (MOTs) of 39 K/ 87 Rb to overcome the light-assisted losses of 39 K atoms. Gray molasses cooling on the D1 line of the 39 K is used to effectively increase the phase density, which improves the loading efficiency of 39 K into the quadrupole magnetic trap. Simultaneously, the normal molasses are employed for 87 Rb. After the microwave evaporation cooling on 87 Rb in the optically plugged magnetic trap, the atoms mixture is transferred to a crossed optical dipole trap, where the collisional properties of the two species in different combinations of the hyperfine states are studied. The dual species BECs of 39 K and 87 Rb are obtained by further evaporative cooling in optical dipole trap at a magnetic field of 372.6 G with the background repulsive interspecies scattering length a KRb = 34 a0 (a0 is the Bohr radius) and the intraspecies scattering length aK = 20.05 a0.