Timing analysis of PSR J1705-1906 using data from Nanshan 25-m and Parkes 64-m radio telescopes, which span over fourteen years, shows that the pulsar exhibits significant proper motion, and rotation instability. We updated the astrometry parameters and the spin parameters of the pulsar. In order to minimize the effect of timing irregularities on measuring its position, we employ the Cholesky method to analyse the timing noise. We obtain the proper motion of -77(3) mas yr(-1) in right ascension and -38(29) mas yr(-1) in declination. The power spectrum of timing noise is analyzed for the first time, which gives the spectral exponent alpha = -5.2 for the power-law model indicating that the fluctuations in spin frequency and spindown rate dominate the red noise. We detect two small glitches from this pulsar with fractional jump in spin frequency of Delta v/v similar to 2.9 x 10(-10) around MJD 55199 and Delta v/v similar to 2.7 x 10(-10) around MJD 55953. Investigations of pulse profile at different time segments suggest no significant changes in the pulse profiles around the two glitches.