Herein, from first‐principles calculations, the phase diagram of the low‐spin (LS) state of BiCoO3 is scrutinized. The phonon‐dispersion curves of the cubic phase are analyzed to identify all the possible unstable modes and assessed the energy gain of the resulted distorted phases. In the findings, the presence of similar phases is revealed in both LS and high‐spin (HS) states, including ferroelectric and octahedra rotations distortions. However, the relative energy ordering of these phases differs significantly between the two states. Notably, the energy gain from mode condensation is considerably less pronounced in the LS case compared to HS state. Furthermore, it is identified that the common Pnma phase is the ground state of the LS state of BiCoC3, closely followed by the Imma octahedra rotation phase and the R3c ferroelectric phase, hence, different from the P4mm ferroelectric ground state of the HS state.