A simple technique of measuring microwave superconductor surface impedance using a dielectric resonator has been developed for small size samples (less than 5 mm x 5 mm). This method has advantages of simplicity to perform, nondestructive analysis, flexibility in sample size, and convenient experimental setup. YBCO (123) high-T-c superconducting films have been measured to verify the method. The measurements have been performed at 14.4 GHz and 77 K.