The linear conversion theory of laser produced plasma filaments is studied in this paper. By calculating the energy flux of the second harmonic emission on the basis of the planar wave-plasma interaction model, it has been found that there exists no 2ω0 harmonic emission in the direction perpendicular to the deasity gradient, in contradiction with, the experiments. Therefore, we have proposed a linear conversion theory on the second harmonic emission from a plasma filament and discovered the intense 2ω0 harmonic emission in the dixoction perpendicular to tiie density gradient. This is in agreement with the experiments.