In recent literature, different approaches have been proposed to use graphemes as subword units with implicit source of phoneme information for automatic speech recognition. The major advantage of using graphemes as subword units is that the definition of lexicon is easy. In previous studies, results comparable to phoneme-based automatic speech recognition systems have been reported using context-independent graphemes or context-dependent graphemes with decision trees. In this paper, we study both context-independent and context-dependent grapheme-based automatic speech recognition systems. Experimental studies conducted on American English continuous speech recognition task show that systems using context-independent grapheme units perform fairly poor, while their performance can be improved by incorporating phonetic knowledge. However, systems using only context-dependent graphemes can yield competitive performance (even better) when compared to state-of-the-art phoneme-based automatic speech recognition.