We study the application of a special class of low-density parity-check codes to the wiretap channel. We construct a randomized coding scheme based on serially concatenated low-density generator matrix codes and their duals extending the approach used for convolutional and turbo codes. Furthermore, we propose an efficient iterative decoder for this scheme utilizing a joint iterative message passing algorithm. We demonstrate via numerical examples that this approach outperforms other available practical coding alternatives for the Gaussian wiretap channel in terms of the resulting security gap.