  In this paper, we investigate pulsating string solutions within the context
of a two-parameter $\chi$-deformed $\mathcal{R} \times S^2$ background. We
derive the energy and oscillation number relation for the deformed $\mathcal{R}
\times S^2$ in a short string limit. Additionally, we derive the first-order
perturbation equation for a pulsating string in this specific background. As a
special case of the two-parameter deformed background, we examine the stability
of the pulsating string solution in one-parameter deformed $\mathcal{R} \times
S^2$ and $AdS_3$ background by setting one of the deformation parameters to
zero.
