We propose a new word embedding method called word-like character n-gram embedding, which learns distributed representations of words by embedding word-like character n-grams. Our method is an extension of recently proposed segmentation-free word embedding, which directly embeds frequent character n-grams from a raw corpus. However, its n-gram vocabulary tends to contain too many non-word n-grams. We solved this problem by introducing an idea of expected word frequency. Compared to the previously proposed methods, our method can embed more words, along with the words that are not included in a given basic word dictionary. Since our method does not rely on word segmentation with rich word dictionaries, it is especially effective when the text in the corpus is in unsegmented language and contains many neologisms and informal words (e.g., Chinese SNS dataset). Our experimental results on Sina Weibo (a Chinese microblog service) and Twitter show that the proposed method can embed more words and improve the performance of downstream tasks.