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In the present study we have performed lattice Boltzmann simulations of an electro-conjugate fluid in order to elucidate the mechanism for inducing a strong microjet between positive and negative electrodes in the situation of a high external electric field. It has been assumed that charges are injected from the surface of a positive electrode where electric fields are significantly concentrated. The mechanism due to these injected charges has mainly been assessed as an essential factor for the occurrence of a strong microjet. In the present numerical simulations, the lattice Boltzmann equations and the basic equation for charge densities have simultaneously been solved for obtaining the flow field and the charge density distribution, respectively. The main results obtained here are summarized as follows. A strong microjet is possibly generated between the positive and the ground electrodes in the situation where Coulomb forces are much more dominant than viscous forces. A microjet starts to occur at the position of the injected charges, grows along with the fluid flow, collides with the ground electrode, and flows away from the electrode in an oblique direction relative to the center line connected between the electrodes. The flow rate induced due to the occurrence of a strong microjet increases approximately in proportion to the increasing external electric field strength. From good agreement with the corresponding experimental result in regard to the velocity vectors of a microjet, we may conclude that the mechanism for inducing a strong microjet in an electro-conjugate fluid is the interaction between the injected charges from the positive electrode and a high external electric field.