We designed optical systems for a mobile phone camera using a spherical SELFOC lens and an aspherical plastic lens. Since the radial index distribution gives an additional design parameter for optical design, an aspheric lens could be replaced by a spherical lens. The imaging performances of the design were compared with conventional 2P design composed of two aspherical plastic lenses. In the first stage of study, we designed 1GRIN 1P lenses by using commercially available SELFOC materials. But, the conventional 2P lenses had better performance than the 1GRIN 1P lenses. In the 1GRIN 1P designs, the performance depends on index variation of GRIN material, the larger variation gives the better performance. Hence, we tried to design by using fictitious GRIN materials which have large index variation. We found if the index variation could be increased to about 3 times that of currently available SELFOC materials, the 1GRIN 1P lens will have equivalent or better performance than the conventional 2P design.