We propose an iterative decision-directed joint frequency offset (FO) and channel estimation algorithm in a known symbol padding (KSP) orthogonal frequency division multiplexing (OFDM) system, where the guard interval is filled with pilot symbols. Besides those time domain pilot symbols, some additional pilot symbols are transmitted on the pilot carriers. The decision-directed algorithm is initialized by pilot-aided FO estimation without channel knowledge. We propose a possible initialization algorithm that operates in the frequency domain (FD). After the initialization phase, the iterative decision-directed estimation algorithm is applied. For the channel estimation step, an existing pilot-aided channel estimation algorithm is extended to a decision-directed algorithm which uses the Fast Fourier Transform outputs at both the pilot and data carrier positions. For the uncoded case, the proposed iterative decision-directed joint FO and channel estimation algorithm reaches the bit error rate performance of a receiver with perfect synchronization and perfect channel knowledge. For a coded system, there is small loss in performance of less than 1 dB when our proposed algorithm is applied compared to a receiver with perfect knowledge about the FO and the channel.