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Let $H_{\\alpha,V}$ be the Sturm Hamiltonian with frequency $\\alpha$ and coupling $V$, $\\Sigma_{\\alpha,V}$ be the spectrum of $H_{\\alpha,V}$. The fractal dimensions of the spectrum have been determined by Fan, Liu and Wen (Erg. Th. Dyn. Sys.,2011) when $\\{a_n\\}_{n\\ge1}$ is bounded. The present paper will treat the most difficult case, i.e, $\\{a_n\\}_{n\\ge1}$ is unbounded. 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