Excess frequency noise induced by mechanical vibration is the dominant noise source at low Fourier frequencies in fiber-delay-line stabilized lasers. To resolve this problem, a double-winding fiber spool is designed and implemented that has ultralow acceleration sensitivity in all spatial directions. By carefully choosing the optimal geometry parameters of the fiber spool, we achieve acceleration sensitivity of 8 × 10 ¹¹/g and 3 × 10 ¹¹/g (g denotes the gravitational acceleration) in axial and radial directions, respectively.