In this paper, we will consider subadditive functions that take an important place not only in mathematics but also in physics and many other fields of science. Subadditive functions are very important also in economics and, specifically, in financial mathematics where subadditive discount functions describe certain behaviors in intertemporal choice and its anomalies. For example, some properties and characterizations of subadditive discount functions can be found in [11]. We establish Hermite-Hadamard-like inequalities for subadditive functions. Moreover, by using an integral identity together with some well known integral inequalities, we obtain several new inequalities for subadditive functions. Moreover, using subadditive functions we give some examples for the Hermite-Hadamard type inequalities. Some applications to special means of real numbers are also given. Especially, it should be noted that the results obtained in this paper coincide with previously obtained results in the literature under certain conditions.