In the present article we obtain the approximation properties of Szász-type operators by use of wavelets in quantum calculus. We construct the Szász-type operators by q-calculus and introduce the Kantrovich variant of this operator by wavelets, then obtain the $L_{p}$ -approximation for $1\leq p \leq \infty $ . We obtain some characterization of second-order Lipschitz function spaces. We use the Ditzian-Totik K-functional and obtain some inequalities in $L_{p}$ spaces. Finally, in the sense of Haar basis for all $1\leq k \leq \mathcal{L} \in \mathbb{N}$ , $0< q<1$ and $0\leq x \leq \frac{2}{(1-q)[m]_{q}}$ , the q-Szász type operators by wavelets as follows: \( \left (\mathcal{W}_{m,k,q} \; g\right )(x)= \frac{1}{\mathcal{E}_{q}^{[m]_{q} x}} \sum _{k=0}^{\infty } q^{\frac{k(k-1)}{2}} \frac{([m]_{q} x)^{k}}{[k]_{q}!} \int _{0}^{\Omega } g\left ( \frac{t+[k]_{q}}{[m]_{q}}\right )\lambda \left (t\right )\mathrm{d}_{q}t. \)
