This paper introduces a vision-based automatic system (VAMS) for non-contact measurement of morphometric characteristics of flatfish, such as total length (TL), body width (BW), height (H), and weight (W). The H and W are simply measured by a laser displacement and a load cell, respectively. The TL and BW are measured by a proposed morphological image processing algorithm. The proposed algorithm cans measurement, when the tail of flatfish is deformed, and when it is randomly oriented. In the experiment, the average and maximum measurement errors were recorded, and standard deviations and coefficients of variation (CVs) for the measurements were calculated. From those results, when flatfish the TL measurements had an average of 266.844 mm, a standard deviation of 0.351 mm, a CV of 0.131%, and a maximum error of 0.87 mm with straightened flatfish ($TL_A$ : 267 mm, $BW_A$ : 141 mm), and when flatfish of different sizes were measured, the errors in the TL and BW measurements were both about 0.2 %. Using a single conveyor, the VAMS can process up to 900 fishes per hour. Moreover, it can measure morphometric characteristics of flatfish with a TL of up to 500 mm.