In this paper, motivated by Kamran et al. [Mathematics, 5(19), (2017),
7 pages] we introduce the notion of parametric $(b,
\theta)$-metric space as an extended form of parametric
$b$-metric space, which was introduced by Hussain et al.[J.
Nonlinear Sci. Appl., 8 (2015), 719–739] and improve the results of
Alsulami et al.[Abstract and Applied Analysis, (2014), Article ID
187031, 10 pages] and others in such space. We also apply our result
to establish an existence of solution of integral equation.