This paper presents a track-before-detect (TBD) algorithm for detection of unknown quantity of targets with parabolic tracks. First, eliminate large number of clutters orderly by expanded trellis and the method of mean power. And then get candidate parabolas by Randomized Hough Transform (RHT). The true tracks of the targets are extracted successfully by a strategy of outliers eliminating at last. Experimental results indicate that the proposed algorithm is capable of detecting multiple targets without the assumptions of an upper bound to the number of targets.