For body weight (BW) and morphological traits measured repeatedly during growth in Japanese flounder, random regression models (RRMs) were constructed to genetically analyse growth curves and relative growth of morphological traits to BW or body length (BL). In the RRM of growth curves, genetic effects were optimally modelled using Legendre polynomials of two orders for six growth traits. Family and permanent environmental effects remained constant for morphological traits, whereas family effects changed linearly for BWs. During the measuring periods, the heritabilities of the traits increased with age and ranged from 0.256 to 0.843 for BW, 0.379 to 0.806 for body height, 0.338 to 0.773 for BL, 0.286 to 0.665 for head length, 0.159 to 0.708 for length of caudal fin and 0.335 to 0.774 for width of caudal peduncle. Genetic correlations for each trait decreased with increased lag in days of age. In the RRM of relative growth, all morphological traits analysed were significantly associated with BW and BL. The heritabilities for the allometries of morphological traits to BWs ranged from 0.251 to 0.755, whereas those to BLs ranged from 0.412 to 0.871. The majority of genetic correlations among these allometry scalings were negative. These estimated parameters can be utilized to not only guide the efficient selection of traits, but also to genetically regulate synchronous growth of body shape with BW in Japanese flounder.