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A new JEC finite-different time-domain algorithm for plasma at high collision frequencies is derived using the time piecewise linear extrapolation for electric field and the recursive convolution relationship between the current density and the electric field (JEC). A simple approach for error analysis is presented to compare the errors of the new method and some other existing methods. The results show that the original JEC method is only suitable for plasma with low collision frequencies, and the new method can greatly improve the accuracy over the original JEC method while maintain relative high computational efficiency. The high accuracy of the new method and the effectiveness of error analysis are also confirmed by computing the interaction of electromagnetic waves with a one-dimension plasma slab.