We report the production of $^{39}$K and $^{87}$Rb Bose-Einstein condensates (BECs) in the lowest hyperfine states $| F=1,m_{F}=1 rangle$ 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 $a_{0}$ ($a_{0}$ is the Bohr radius) and the intraspecies scattering length $a_{K}$ = 20.05 $a_{0}$.
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