He deserves to win the cup.Where deserve is a catenative verb which can be followed directly by another verb, in this case in the "to" infinitive form.
Most of these verbs demand that the following verb be in one or the other (infinitive or gerund) form only. A few can take both forms, but sometimes there is a difference in meaning.
They are called catenative from their ability to form chains.
We promised to agree to try practicing playing tennis more often.
See wiktionary for a list of catenative verbs.