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We have studied the $CP$ violation discovery reach in neutrino oscillationexperiment with superbeam in presence of non-standard interactions of neutrinoswith matter for both short and long baselines. For the most important channelof oscillation ($\nu_\mu \rightarrow \nu_e$) for $CP$ violation discovery thereis significant effect in the oscillation probability particularly due to NSIs'$\varepsilon_{e\mu}$ and $\varepsilon_{e\tau}$ for longer baseline and higherenergy in comparison to other NSIs'. Interestingly for these two NSIs' (forreal and higher allowed values) there is possibility of better discovery reachof $CP$ violation than that with only Standard Model interactions of neutrinoswith matter provided that NSI values are known. For complex NSIs' we have shownthe $CP$ violation discovery reach in the plane of Dirac phase $\delta$ and NSIphase $\phi_{ij}$. Our analysis indicates that for some values of some NSIphases total $CP$ violation may not be observable for any values of $\delta $.

Non-standard interaction effect on $CP$ violation in neutrino oscillation with super-beam