As an Earth co-orbital asteroid, (469219) Kamo\`oalewa is a near earth object (NEO) with high value of research and one of the targets explored by the first Chinese asteroid exploration mission. Given its orbit characteristics, we build a refined dynamical model for this asteroid. In the model, figure effects induced by nonspherical gravitational fileds of the Sun, the Earth and the Moon are taken into account. On the basis of the dynamical model of the asteroid (469219) Kamo\`oalewa, its orbit is determined with optical data from 2004 to 2018 downloaded from the Minor Planet Center (MPC) database. The root mean square error of post-fit residuals is about 0.2 arc second (comparable with that of JPL/Horizons), and the post-fit residuals of optical observations in 2004 are decreased. At the end, we implement error analysis on the asteroid (469219) Kamo\`oalewa's orbit in detail, and also predict its orbit error at the time interval between 2020 and 2025.