Abstract: | The relationship between charge-density-wave (CDW) and superconductivity (SC), two vital physical phases in condensed matter physics, has always been the focus of scientists' research over the past decades. Motivated by this research hotspot, we systematically studied the physical properties of the layered telluride chalcogenide superconductors CuIr$_{2-x}$Al$_{x}$Te$_{4}$ ($0 leqslant x leqslant 0.2$). Through the resistance and magnetization measurements, we found that the CDW order was destroyed by a small amount of Al doping. Meanwhile, the superconducting transition temperature ($T_{rm c}$) kept changing with the change of doping amount and rose towards the maximum value of 2.75 K when $x=0.075$. The value of normalized specific heat jump ($Delta C/gamma T_{rm c}$) for the highest $T_{rm c}$ sample CuIr$_{1.925}$Al$_{0.075}$Te$_{4}$ was 1.53, which was larger than the BCS value of 1.43 and showed the bulk superconducting nature. In order to clearly show the relationship between SC and CDW states, we propose a phase diagram of $T_{rm c}$ vs. doping content. |