We consider the quasi-periodic Jacobi operator $H_{x,\omega }$ in $l^2(\mathbb {Z})$ : $(H_{x,\omega }\phi )(n)=-b(x+(n+1)\omega )\phi (n+1)-b(x+n\omega )\phi (n-1)+a(x+n\omega )\phi (n)=E\phi (n)$, $n\in \mathbb {Z}$, where $a(x),\ b(x)$ are analytic functions on $\mathbb {T}$, $b$ is not identically zero, and $\omega $ obeys some strong Diophantine condition. We consider the corresponding unimodular cocycle. We prove that if the Lyapunov exponent $L(E)$ of the cocycle is positive for some $E=E_0$, then there exist $\rho _0=\rho _0(a,b,\omega ,E_0)$, $\beta =\beta (a,b,\omega )$ such that $|L(E)-L(E')|<|E-E'|^\beta $ for any $E,E'\in (E_0-\rho _0,E_0+\rho _0)$. If $L(E)>0$ for all $E$ in some compact interval $I$, then $L(E)$ is Hölder continuous on $I$ with Hölder exponent $\beta =\beta (a,b,\omega ,I)$. In our derivation we follow the refined version of the Goldstein-Schlag method [?] developed by Bourgain and Jitomirskaya [?].