In analog and mixed signal design, exact matching requirement is critical for correct functionality of analog devices. However, due to the excessive complexity, it is difficult to consider exact matching constraint in detailed routing stage. This paper presents a novel gridless detailed routing algorithm, which efficiently obtains the optimized detailed routing solutions for a given set of nets with exact matching constraints. The gridless routing algorithm is based on an efficient non-uniform grid model, which enables the obstacles avoidance. To test the eectiveness of the gridless routing algorithm, a grid routing algorithm and a modied exact matching routing algorithm from  are also implemented. Experimental results show signicant improvements of the proposed gridless routing algorithm over the other two algorithms in both QOR and runtime.