Space shift keying (SSK), conveying data symbols via only the antenna indices, is a new modulation technique for low-complexity implementation of multiple-input multiple-output (MIMO) systems. SSK can be combined with the orthogonal frequency division multiplexing (OFDM) technique to improve the capacity and reliability of transmission. However, the SSK MIMO-OFDM systems also inherit from OFDM systems the drawback of a high peak-to-average power ratio (PAPR) of the transmitted signal. To overcome this problem, in this paper, the special information-conveying mode of SSK is utilized and a fast-converged gradient-based PAPR reduction method which exploits the phase freedom of the transmitted SSK MIMO-OFDM signal in the frequency domain is proposed. Simulation results show that the proposed improved gradient-based method (GBM) achieves a superior PAPR performance, as compared to the promising discrete phase set based schemes such as selected mapping method (SLM) and flipping method. Besides the considerable PAPR reduction, the improved GBM also enjoys other advantages such as low complexity, and neglectable performance loss.