The initial orbit determination (IOD) of the very-short-arc (VSA) and the association between them are the key steps for expanding the catalogue with optical observations obtained from ground-based or space-based telescopes. For this reason, the distance search method for IOD and the geometrical method for their association were proposed. With optical observations from ground-based small telescopes array at Changchun Observatory, National Astronomical Observatories, China Academy of Sciences in Changchun and simulated observations from space-based telescope, the IOD and the association between the IODs are performed. The successful rates of getting an IOD solution for an optical arc with the distance search method is about 90%. For two kinds of observations. The IOD association results show that the true positive (assert that they are from same object for IODs from a same object) rate is over 80% in most cases. Ant the effects on the association accuracy of filtered different IODs are analyzed in depth. With actual optical observations obtained at Changchun, the results of IOD and their association show the validity of the IOD method and association method used in this paper and they can be used to expand the space object catalogue.