In order to study the potential associated with high precision CCD astrometry of irregular satellites, we have acquired experimental observations of Himalia, the sixth and irregular satellite of Jupiter. A total of 185 CCD observations were obtained by using the 2.4 m and 1 m telescopes administered by Yunnan Observatories over ten nights. Preliminary analysis of the observations were made, including geometric distortion, atmospheric refraction, and also the phase effect. All positions of Himalia are measured relative to the reference stars from the catalog UCAC4 in each CCD field of view. The theoretical positions of Himalia were retrieved from the Institute de Mechanique Celeste et de Calcul des Ephemerides, while the positions of Jupiter were obtained based on the planetary ephemeris INPOP13c. The results show that the means of observed minus computed (O - C) residuals are -0.004" and -0.002" in right ascension and declination, respectively. The standard deviations of (O - C) residuals are estimated to be about 0.04" in each direction.