The high-power fiber laser pumped by laser diodes (LDs) has the advantages of high efficiency, small size, light weight, and good stability, and has been widely used in many fields such as industrial processing. To improve the absorption rate of pump laser, the 915 nm and 976 nm LDs are commonly used as the pump source of the traditional fiber lasers. The quantum defect and pump absorption coefficient are comparatively high in the fiber lasers pumped by these LDs, which leads to low transverse mode instability (TMI) threshold. To improve quantum efficiency and potential TMI threshold, the fiber laser directly pumped by LDs with wavelength longer than 1010 nm is proposed. An oscillating-amplifying integrated laser was built, and 2.05 kW output laser with beam quality M² of 1.7 was realized when the fiber laser was pumped by 1010 nm LDs with maximum pump power of 2.56 kW. In the future, fiber laser with higher output power and better beam quality can be realized by increasing the pump power and optimizing the fiber characteristics.