This paper explores the possibility to use grapheme-based word and sub-word models in the task of spoken term detection (STD). The usage of grapheme models eliminates the need for expert-prepared pronunciation lexicons (which are often far from complete) and/or trainable grapheme-to-phoneme (G2P) algorithms that are frequently rather inaccurate, especially for rare words (words coming from a~different language). Moreover, the G2P conversion of the search terms that need to be performed on-line can substantially increase the response time of the STD system. Our results show that using various grapheme-based models, we can achieve STD performance (measured in terms of ATWV) comparable with phoneme-based models but without the additional burden of G2P conversion.