Comet Tsuchinshan (1977q) was discovered at Purple Mountain Observatory on Nov. 3, 1977. The osculating orbital elements (referred to the barycenter of the sun and Mercury) given in table 1 are derived from 42 observations Nov. 3, 1977 to Jan. 10, 1978 at our observatory and abroad, taking into account the perturbations of all major planets. In all the observations the rms residual is 1.″78. Our observations are also published in table 2. With the elements thus obtained, the appropriate ephemerides in recent years have been calculated and listed in table 4. And then, in consideration of accurate perturbations, we compute the original and future orbits (referred to the center of mass of solar system) while the comet is about 60 A. U. from the sun. The results that both the original and future orbits are hyperbolicaare given in table 5 and may be compared with the osculating elements. Nevertheless, the two months observed interval for determining orbit is short. In order to obtain the more reliable conclusion, it is necessary to make some efforts for increasing the observed arc.