A new type of ECR ion source—a gasdynamic ECR ion source—has been recently developed at the Institute of Applied Physics. The main advantages of such device are extremely high ion beam current with a current density up to 600–700 emA/cm2 in combination with low emittance, i.e., normalized RMS emittance below 0.1 π mm mrad. Previous investigations were carried out in pulsed operation with 37.5 or 75 GHz gyrotron radiation with power up to 100 kW at SMIS 37 experimental facility. The present work demonstrates the first experience of operating the gasdynamic ECR ion source in CW mode. A test bench of SMIS 24 facility has been developed at IAP RAS. 24 GHz radiation of CW gyrotron was used for plasma heating in a magnetic trap with simple mirror configuration. Initial studies of plasma parameters were performed. Ion beams with pulsed and CW high voltage were successfully extracted from the CW discharge. Obtained experimental results demonstrate that all advantages of the gasdynamic source can be realized also in CW operation.