Verb phrase complements in English grammar are words and phrases that complete the meaning of the verb phrase.
Verb phrase complement is a grammatical function.
The grammatical forms that can function as the verb phrase complement in English grammar are the prepositional phrase and the verb phrase.
The preposition of a prepositional verb functions as a verb phrase complement. The infinitive following catenative verbs functions as a verb phrase complement.
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Hopper, Paul J. 1999. A short course in grammar. New York: W. W. Norton & Company.
Huddleston, Rodney. 1984. Introduction to the grammar of English. Cambridge: Cambridge University Press.