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Within the framework of nonlinear force-free field models, we have developed a relaxation scheme for estimating horizontal electric currents in solar active regions. The test case which uses an analytical solution shows that at each iteration step the average Lorentz force decreases rapidly and the values of ∂Bx/∂z and ∂By/∂z converge well toward analytical ones. As a result the computed horizontal electric currents and analytical ones show good agreement in both distribution and magnitude. This scheme has avoided mathematical singularities along the inversion line Bz = 0 which appeared in the previous extrapolating methods. Then this newly developed scheme is used to analyze the vector magnetogram of a flare-prolific region NOAA 6659. The computational results show the following: (1) The distribution of horizontal electric current and vertical electric current share a similar configuration. (2) Near the separator of a quadrupole field configuration of this active region there is a confined region of strong horizontal electric currents, near which a white-light flare took place on the same day.

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