Aiming at the case of target missing in a short time occurring frequently in target tracking with a single theodolite, Chebyshev polynomial is used to fit and extrapolate the trajectory of the target with the data observed by theodolite. Chebyshev polynomial has a better accuracy than the traditional method of interpolation by comparison. The results of residuals and standard deviation calculated through the least square method show that six-order polynomial has the best fitting accuracy with the error of about 8.226 μm. When the missing distance of theodolite is invalid or the target speed features suddenly changes, the theodolite is able to follow the trajectory of the predicted movement. Experimental results show that this method can be used to fulfill stable target tracking when the theodolite loses the targets within a short scope of time (3~4 s). Recently, this problem is still under theoretical study and cannot be put into engineering practice in the near future.