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We present the size–mass relation of the brightest cluster galaxies (BCGs) at 0.1 < z < 1.4 using the imaging data obtained by the Hyper Suprime-Cam Subaru Strategic Program. Our sample consists of 471 photometrically selected BCGs with stellar mass log M */M⊙ = 11–12. We measure the size of the BCGs using i -band imaging and model fits based on a single Sérsic light profile. Stellar masses are determined through spectral energy distribution fitting using Sérsic-modelled photometry data across five optical bands (grizy). The size–mass scaling relation of BCGs is |$r_\mathrm{ e}\propto M_*^{0.73-1.00}$| at z < 1, with a slope that does not evolve significantly. The slope of the size–mass relation for BCGs is steeper than other non-BCG galaxies, which implies that BCGs are a special galaxy population. The size of BCGs at a given stellar mass evolves rapidly as ∝ (1 + z)−1.58 ± 0.13 and increases with redshift by a factor of 2.5 from z ∼ 1.2 to z ∼ 0.2. The rapid size growth is in agreement with semi-analytical model results, indicating that the BCG growth is dominated by frequent minor mergers. Furthermore, we explore the size–mass relationship of BCGs with respect to the halo mass of the cluster and find there is no significant correlation, which might imply that a dependence on the environment predominantly affects the outer envelope of the BCGs. [ABSTRACT FROM AUTHOR]