By measuring the temperature dependence of the resistance, we investigated the effect of Cu doping on superconductivity (SC) in Cu-doped TaSe$_3$ in which the charge density wave (CDW) transition is induced by Cu doping. We observed an emergence of a region where the SC transition temperature ($T_mathrm{C}$) decreased in samples with higher Cu concentrations and found that the region tended to expand with increasing Cu concentration. In addition, the temperature dependence of the upper critical field ($H_mathrm{C2}$) of Cu-doped TaSe$_3$ was found to differ from that of pure TaSe$_3$. Based on these experimental results and the fact that the SC of TaSe$_3$ is filamentary, we conclude that SC is suppressed locally by Cu doping and competes with the CDW in Cu-doped TaSe$_3$. The resistance anomaly due to the CDW transition was extremely small and the size of the anomaly was enhanced with increasing Cu concentration but the temperature at which the anomaly appeared hardly changed. This result of the anomaly and the local suppression of SC imply that the induced CDWs are short-range order in the vicinity of Cu atoms. We also discuss the effect of the pinning of CDWs on the relationship between SC and short-range order CDWs.
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