Abstract: The fourth phase of China's lunar exploration project will build the first lunar terrestrial Space VLBI test system composed of a 4.1 m antenna on Chang'e 7 relay satellite and a ground-based radio telescope. Different from the ground-based VLBI system, due to the influence of relay satellite orbit disturbance and equipment delay, the predicted delay model of radio source may be quite different from the actual delay, which can not guide the relevant processors VLBI-processing units to work properly. In this paper, a radio source fringe search algorithm for Space VLBI is proposed, so as to improve the weak signal receiving ability of space small aperture antenna and to satisfy the need of using quadratic delay model to ensure long-time integration accuracy. Firstly, a two-dimensional search grid about delay and delay rate is established, using the prior delay and delay rate information of each grid point, the linear delay is constructed to process the original data in different time periods. Then the residual delay and delay rate are searched by two-dimensional Fourier transform to determine the grid point corresponding to the maximum correlation amplitude value. Finally, the quadratic delay model is reconstructed by using the delay corresponding to the grid point. The algorithm can be applied to the radio source fringe search of the ground air baseline of the RadioAstron project.