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Many researchers have paid attention to the shallow water wave model Camassa- Holm (CH) equation over the last 2 decades. The single periodic solution to the CH equation based on the Hirota bilinear method had been presented in our previous work. The quasi-periodic solution in genus 2 and its asymptotic behavior were given. First, the parameters appearing in the bilinear equation system were rearranged, such as the coordinate transformation, the extended bilinear form, the Riemman theta function and so on. Then the quasi-periodic solution to the CH equation was obtained, which was expressed in the form of the Riemann theta function in genus 2. Second, the asymptotic behavior of the quasi-periodic solution was discussed. It is shown that this solution can degenerate into the CH equation’s 2-soliton solution. [ABSTRACT FROM AUTHOR]