Based on the special two-dimensional flexible structure，graphene has excellent optical and electrical properties. With the finite element method, we theoretically investigated modulation of the optical field of graphene covered microfiber. By changing the overlay angle, the symmetrical structure of fiber was destroyed to provide the microfiber with birefringence. The value of birefringence is a function of overlay angle. The chemical potential of graphene can be modulated and the light transmission of optical fiber can be switched by changing the external voltage. We designed a graphene covered microfiber based electrical absorption modulator and proceeded the performance analysis. Numerical simulations show that when the overlay angle is 270° and the incident wavelength is 1550 nm,the birefringence can be up to 1.23×10-3. When the electric absorption modulator works at the wavelength of 1550 nm, its length is 18 μm, the extinction radio is 7 dB, the 3 dB bandwidth reaches 927 MHz, and the insert loss is 0.58 dB.