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Abstract We study the chirally imbalanced hot and dense strongly interacting matter by means of the Dyson-Schwinger equations (DSEs). The chiral phase diagram is studied in the presence of chiral chemical potential μ 5. The chiral quark condensate ψ ¯ ψ $$ \left\langle \overline{\psi}\psi \right\rangle $$ is obtained with the Cornwall-Jackiw-Tomboulis (CJT) effective action in concert with the Rainbow truncation. Catalysis effect of dynamical chiral symmetry breaking (DCSB) by μ 5 is observed. We examine with two popular gluon models and consistency is found within the DSE approach, as well as in comparison with lattice QCD. The critical end point (CEP) location (μ E , T E ) shifts toward larger T E but constant μ E as μ 5 increases. A technique is then introduced to compute the chiral charge density n 5 from the fully dressed quark propagator. We find the n 5 generally increases with temperature T , quark number chemical potential μ and μ 5. Since the chiral magnetic effect (CME) is typically investigated with peripheral collisions, we also investigate the finite size effect on n 5 and find an increase in n 5 with smaller system size.