  We consider the approximate properties of tight wavelet frames on Vilenkin
group $G$. Let $\{G_n\}_{n\in \mathbb{Z} }$ be a main chain of subgroups, $X$
be a set of characters. We define a step function $\lambda({\chi})$ that is
constant on cosets ${G}_n^\bot\setminus{G}_{n-1}^\bot$ by equalities $\lambda
({G}_n^\bot\setminus{G}_{n-1}^\bot)=\lambda_n>0$ for which
$\sum\frac{1}{\lambda_n}<\infty$.
  We find the order of approximation of functions $f$ for which
  $\int_X|\lambda( {\chi})\hat{f}(\chi)|^2d\nu(\chi)<\infty$. As a corollary,
we obtain an approximation error for functions from Sobolev spaces with
logarithmic weight.
