Erbium-doped hole-assisted lightguide fiber (EDHALF) is composed of a high-index core doped with erbium, a low index cladding and a small number of air holes surrounding the core. The finite element method is applied for solving the modal field of the EDHALF. The numerical calculation methods of the cutoff wavelength and mode field diameter are described in detail. The modified average population inversion iteration method is proposed for calculating the gain and noise figure of erbium-doped fiber amplifiers. The effects of the air holes on EDHALFs' cutoff wavelengths, mode field diameters and the gain coefficients of fiber amplifiers are studied. It's found that decreasing the relative hole-to-core spacing can make the cutoff wavelength move to shorter wavelength and decrease the mode field diameter. When the relative size of air holes is relatively large, further enlarging it only slightly changes the cutoff wavelength, mode field diameter and the maximum of the gain coefficient. Finally, four structural parameters, namely the EDHALF-core radius, the refractive index difference between the core and cladding, the relative hole-to-core spacing and the relative size of air holes are optimized in terms of the design criteria, which take into account the cutoff wavelengths of fundamental mode and the second order mode, the gain and noise figure of fiber amplifiers and the splice loss between the EDHALF and the conventional single-mode fiber.