We have explored non-canonical scalar field model in the background of non-flat D-dimensional fractal Universe on the condition that the matter and scalar field are separately conserved. The potential V , scalar field φ, function f , densities, Hubble parameter and deceleration parameter can be expressed in terms of the redshift z and these depend on the equation of state parameter w φ . We have also investigated the cosmological analysis of four kinds of well known parametrization models. In graphically, we have analyzed the natures of potential, scalar field, function f , densities, the Hubble parameter and deceleration parameter. As a result, the best fitted values of the unknown parameters (w 0 , w 1 ) of the parametrization models due to the joint data analysis (SNIa+BAO+CMB+Hubble) have been found. Furthermore, the minimum values of χ 2 function have been obtained. Also we have plotted the graphs for different confidence levels 66%, 90% and 99% contours for (w 0 , w 1 ) by fixing the other parameters.