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This letter introduces a kind of algebraic fractal model-Paretian Poisson process to the field of sea spike modeling and target detection. Sea spikes are strong rapidly varying echoes lasting for up to some seconds, which can be judged from the clutter background according to three parameters, i.e., the spike amplitude, the minimum spike width, and the minimum interval between spikes. Paretian Poisson process performs well in describing a power-law connection between positive-valued measurements and their occurrence frequencies. In this letter, Paretian Poisson process is used for modeling the relation between the spike durations and the spikes' occurrence frequencies. By the verification of X-band radar data, we find that Paretian Poisson process can well model sea spikes, and its parameters, the Paretian exponent and the residual sum of squares, have the potential for distinguishing targets from sea spikes. Consequently, a target detection method is proposed, and the detecting performance is analyzed. The results show that the proposed method performs well in target detection except the high requirement of the quantity of samples.