To clarify the growth mechanism of YBa 2Cu 3O 7− X (Y123) crystals in the multi-coated film fabricated by the trifluoroacetates–metal organic deposition (TFA–MOD) method, the growth processes of Y123 crystal grains were studied by the experimental method and the numerical method. Microstructures of growing Y123 crystals were revealed through transmission electron microscopy (TEM) observations of the specimens quenched during the growth of Y123 crystals on LaAlO 3 (LAO) substrates. It was observed that some a-axis grains grow among many c-axis grains, and they have some terraces near the initial boundaries of multi-coated layers. The above terraces of a-axis grains were considered to form by the change in c-axis ( c-plane) growth rate of a-axis grains, which may have some dislocations and/or stacking faults. The growth processes and the above microstructures of faceted Y123 crystal grains were also shown by the two-dimensional numerical simulation using c- and a-axes growth rate functions.