By using, the third nearest neighbor modified tight binding approximation and Green's function method, the density of state (DOS) and thermal conductivity of armchair and zigzag BN nanoribbon (BNNRs) are investigated in the presence of an external electric field. The band gap of the both armchair and zigzag BNNRs has a decreasing with increasing the intensity of the applied external electric field. In the higher electric field, the semiconductor metallic transition occurs for both BNNRs. The size and position of the peaks in the DOS spectra are sensitive to the electric field strength. It is found that thermal conductivity changes exponentially with temperature and electric field modifies their behaviors in lower and higher temperature ranges. In the presence of an electric field, the thermal conductivity increases (decreases) in low (high) temperature ranges for both armchair and zigzag BNNRs. By length wide increasing, the thermal conductivity decreases in absence and presence of electric field which in agreement with behaviors of BN bilayers.
