Lightning protection system of a wind turbine blade, whose structure comprises two structural shells (11, 13) including two caps (19, 21) formed by carbon fiber laminates and two spars (15, 17), comprising: - a first subsystem comprising one or more lightning receptors (25, 25') connected to a first conductor cable disposed inside of the wind turbine blade for driving lightning to ground; and - a second subsystem comprising connecting means between the caps (19, 21) and the first conductor cable allowing equipotentializing the lightning protection system in at least two cross sections (22, 23) of the wind turbine blade; characterized in that: - a first subsystem also comprises a second conductor cable arranged inside of the wind turbine blade for driving lightning to ground; - the second subsystem also comprises in each of said cross sections (22, 23) a first lateral lightning receptor arranged on one edge of said cross sections (22, 23) including first internal conducting blocks (36, 37) in the structural shells (11, 13) and first external connectors (56, 57) configured so that they can interconnect electrically the first internal conducting blocks (36, 37); and in each of said cross sections (22, 23) a second lateral lightning receptor arranged at the edge of said cross sections opposite to the edge of the first lateral lightning receptor that includes second internal conducting blocks (34, 35) in the structural shells (11, 13) and second external connectors (54; 55) configured so that they allow to interconnect electrically the second internal conducting blocks (34, 35); - the first internal conducting blocks (36, 37) are connected to the caps (19, 21) by first auxiliary cables (46, 47); - the first conductor cable is connected to one of the first auxiliary cables (46, 47) via a second auxiliary cable; and - a second internal conducting blocks (34, 35) are connected to the caps (19, 21) by third auxiliary cables (44, 45); - a second conductor cable is connected to one of said third auxiliary cables (44, 45) by a fourth auxiliary cable; - a second subsystem further comprises an equipotential bar connected to the first and second conductor cables (41, 43). - a first subsystem comprising one or more lightning receptors (25, 25') connected to a first conductor cable disposed inside of the wind turbine blade for driving lightning to ground; and - a second subsystem comprising connecting means between the caps (19, 21) and the first conductor cable allowing equipotentializing the lightning protection system in at least two cross sections (22, 23) of the wind turbine blade; - a first subsystem also comprises a second conductor cable arranged inside of the wind turbine blade for driving lightning to ground; - the second subsystem also comprises in each of said cross sections (22, 23) a first lateral lightning receptor arranged on one edge of said cross sections (22, 23) including first internal conducting blocks (36, 37) in the structural shells (11, 13) and first external connectors (56, 57) configured so that they can interconnect electrically the first internal conducting blocks (36, 37); and in each of said cross sections (22, 23) a second lateral lightning receptor arranged at the edge of said cross sections opposite to the edge of the first lateral lightning receptor that includes second internal conducting blocks (34, 35) in the structural shells (11, 13) and second external connectors (54; 55) configured so that they allow to interconnect electrically the second internal conducting blocks (34, 35); - the first internal conducting blocks (36, 37) are connected to the caps (19, 21) by first auxiliary cables (46, 47); - the first conductor cable is connected to one of the first auxiliary cables (46, 47) via a second auxiliary cable; and - a second internal conducting blocks (34, 35) are connected to the caps (19, 21) by third auxiliary cables (44, 45); - a second conductor cable is connected to one of said third auxiliary cables (44, 45) by a fourth auxiliary cable; - a second subsystem further comprises an equipotential bar connected to the first and second conductor cables (41, 43).