Cyanobacteriochromes (CBCRs) are cyanobacterial photoreceptors distantly related to the phytochromes sensing red and far-red light reversibly. Only the cGMP phosphodiesterase/Adenylate cyclase/FhlA (GAF) domain is needed for chromophore incorporation and proper photoconversion. The CBCR GAF domains covalently ligate linear tetrapyrrole chromophores and show reversible photoconversion between two light-absorbing states. In most cases, the two light-absorbing states are stable under dark conditions, but in some cases, the photoproduct state undergoes thermal relaxation back to the dark-adapted state during thermal relaxation. In this study, we examined the engineered CBCR GAF domain, AnPixJg2_BV4. AnPixJg2_BV4 covalently binds biliverdin IX-alpha (BV) and shows reversible photoconversion between a far-red-absorbing Pfr dark-adapted state and an orange-absorbing Po photoproduct state. Because the BV is an intrinsic chromophore of mammalian cells and absorbs far-red light penetrating into deep tissues, BV-binding CBCR molecules are useful for the development of optogenetic and bioimaging tools used in mammals. To obtain a better developmental platform molecule, we performed site-saturation random mutagenesis on the Phe319 position. We succeeded in obtaining variant molecules with higher chromophore-binding efficiency and higher molar extinction coefficient. Furthermore, we observed a wide variation in thermal relaxation kinetics, with an 81-fold difference between the slowest and fastest rates. Both molecules with relatively slow and fast thermal relaxation would be advantageous for optogenetic control.