The size of the optical zoom system is important in smartphone camera design, especially as it governs the thickness of the smartphone. We present the optical design of a miniaturized 10× periscope zoom lens for smartphones. To achieve the desired level of miniaturization, the conventional zoom lens can be replaced with a periscope zoom lens. In addition to this change in the optical design, the quality of the optical glass, which also affects the performance of the lens, must be considered. With advancements in the optical glass manufacturing process, aspheric lenses are becoming more widely used. In this study, aspheric lenses are incorporated into a design for a 10× optical zoom lens with a lens thickness of less than 6.5 mm and an eight-megapixel image sensor. Furthermore, tolerance analysis is carried out to prove its manufacturability.