Radar detection of small targets in sea clutter is a particularly demanding task because of the nonstationary characteristic of sea clutter. The track-before-detect (TBD) filter is an effective way to increase the signal-to-clutter ratio (SCR), thus improving the detection performance of small targets in sea clutter. To cope with the nonstationary characteristic of sea clutter, an easily-implemented Bayesian TBD filter with adaptive detection threshold is proposed and a new parameter estimation method is devised which is integrated into the detection process. The detection threshold is set according to the parameter estimation result under the framework of information theory. For detection of closely spaced targets, those within the same range cell as the one under test are treated as contribution to sea clutter, and a successive elimination method is adopted to detect them. Simulation results prove the effectiveness of the proposed algorithm in detecting small targets in nonstationary sea clutter, especially closely spaced ones.