The kinetics of the non-isothermal and isothermal crystallization of the crystalline smectic B phase (soft crystal B, SmBcr) in 4-n-butyloxybenzylidene-4′-n′-octylaniline (BBOA) was studied by a combination of differential scanning calorimetry (DSC), broadband dielectric spectroscopy (BDS) and polarized optical microscopy (POM). On cooling, part of the SmBcr phase undergoes conversion to a crystalline phase and the remainder forms a glassy state; after the glass softens, crystallization is completed during subsequent heating. By analyzing the area of the crystal growing in the texture of SmBcr as a function of time, the evolution of degree of crystallinity, D(t), was estimated. It was demonstrated that upon heating, D(t) follows the same Avrami curve as the crystallization during cooling. Non-isothermal crystallization observed during slow cooling rates (3K/min ≤ ϕ ≤ 5K/min) is a thermodynamically-controlled process with the energy barrier Ea ≈ 175 kJ/mol; however, the crystallization occurring during fast cooling (5 K/min > ϕ ≥ 30K/min) is driven by a diffusion mechanism, and is characterized by Ea ≈ 305 kJ/mol. The isothermal crystallization taking place in the temperature range 274 K and 281 K is determined by nucleus formation.