The objective lens of the optical pickup is widely used in optical storage systems. Holographic optical storage uses holography to record and reconstruct information for storage purposes. The objective lens used in this process requires a high resolution and the commercially available objective lenses do not meet the requirements. Since both recording and reading are on the holographic recording material, the refractive index and thickness of the holographic material will impact the resolution and focusing efficiency of the objective lens. "Dual beam holographic optical storage" requires an objective lens of the optical pickup with high resolution and focusing efficiency in the dual working wavelengths mode of the beam. In order to fulfill such requirements, this study demonstrates the design of a dual-wavelength aspheric objective lens of optical pickup for holographic optical storage which is composed of an aspherical and spherical mirror by using the Zemax OpticStudio. The two working wavelengths are 532nm and 650nm and the focal length is greater than 4mm but less than 6.2mm. The numerical aperture is greater than 0.5, the MTF is greater than 0.4 within the spatial frequency of 900lp/mm, and the root means square of the wave surface difference obtained by focusing on the holographic material is less than 0.07λ. Regarding the above technical indicators, the designed objective lens has a high resolution and imaging quality. This design provides a new idea for the design of holographic optical storage lens.