The sensorless control of interior permanent magnet synchronous motor (IPMSM) based on the conventional linear extended state observer (LESO) does not have sufficient capability to eliminate the steady-state position estimation error. To solve this issue, a frequency adaptive LESO (FA-LESO) is proposed to estimate the back electromotive force (BEMF) accurately. The gains of the proposed observer are designed according to the pre-designed transfer function of a second-order complex-coefficient filter, whose stability is guaranteed by the generalized Routh criterion. The linearized model of the proposed FA-LESO is established and the design guideline of the observer gains is presented. Compared with the conventional LESO, the proposed FA-LESO can eliminate the steady-state position estimation error without any phase compensation. Meanwhile, it exhibits better high-frequency noise immunity without additional filters being required. The feasibility and effectiveness of the proposed FA-LESO are verified by the comparative experiments on a dual three-phase IPMSM platform.