We propose and experimentally demonstrate an ytterbium-doped fiber laser emitting the single high-order cylindrical vector beams with a high efficiency and a high modal purity based on adaptive modal gain control. By the combination of a high-order pump with a self-designed ytterbium-ring doped fiber, modal dependent gain was tailored and specific transverse mode can be selected in the laser cavity. A model based on multimode propagation-rate equations is built up to demonstrate the behaviors of transverse mode competition in the fiber laser. Modal dependent gain of high-order mode pump are simulated numerically, which agree well with our experiment results. The slope efficiency of the fiber laser reaches 79.61% with a low threshold of 47.73mw. The purity of the generated high-order CVBs are in excess of 95%. Such a strategy enables the controllability of modal gain in a fiber laser and reveals the potential to offer a new and promising way to achieve a high-power fiber laser with an arbitrary single high-order transverse modes output.