Provided is an internal hybrid electrochemical cell comprising: (A) a pseudocapacitance cathode comprising a cathode active material that contains a conductive carbon material and a porphyrin compound, wherein the porphyrin compound is bonded to or supported by the carbon material to form a redox pair for pseudocapacitance, wherein the carbon material is selected from activated carbon, activated carbon black, expanded graphite flakes, exfoliated graphite worms, carbon nanotube, carbon nanofiber, carbon fiber, a combination thereof; (B) a battery-like anode comprising lithium metal, lithium metal alloy, or a prelithiated anode active material (e.g. prelithiated Si, SiO, Sn, SnO2, etc.), and (C) a lithium-containing electrolyte in physical contact with the anode and the cathode; wherein the cathode active material has a specific surface area no less than 100 m2/g which is in direct physical contact with the electrolyte.