With a movable quadrupole magnetic trap (QMT) generated by two pairs of partly-overlapped magneto-optical trap (MOT) and transfer coils, a highly efficient transport of cold 87Rb atoms to the atom chip surface is realized. By the QMT movable means of linearly increasing the current in the transfer coils but simultaneously keeping the current in the MOT coils constant, the velocity profile of the moving trap is Blackman-type-like. With this QMT movable scheme, the cold atoms are transferred to the atom chip surface from the MOT center. In the transfer process, the cold atom temperature is increased by about 30 μK, and the transfer efficiency is above 90%. This system provides an appropriate cold atoms source for the atom chip interferometer and also can be used to investigate the interaction between atom and chip surface.