We have developed the experimental apparatus which combines an ion trap with the laser cooling technique in order to detect single ions, which enables one to apply to the trace analysis of the rare isotope such as Ca-41. The characteristics of the ion trap apparatus and a laboratory-made diode laser system were measured and reported. The ions generated by the laser ablation were successfully trapped and the simultaneous irradiations of two different diode lasers were performed to observe the laser cooling of the ions. The spectrum of the fluorescence of the Ca ions had the asymmetrical peak as a function of the laser wavelength, which showed the temperature of the Ca ions was decreased. The outlook to observe the single Ca-41 was discussed.