A verb phrase is a phrase consisting of a verb. All the phrases linked grammatically to that verb except a subject are also part of that verb phrase. Here is an example test for verb phrases:
Any sequence which can fill the blank to make a grammatical sentence will probably be a verb phrase.
Alice is a writer. (verb phrase: is a writer)
Alice wants to be a writer. (verb phrase: wants to be a writer)
Alice is working in the garden. (verb phrase: is working in the garden)
Alice has told me that she will not come. (verb phrase: has told me that she will not come.)
Alice will be vacationing is Mexico. (verb phrase: will be vacationing in Mexico)
A verb phrase can contain a smaller verb phrase in it. For example, the verb phrase ‘is working in the garden’ contains the smaller verb phrase ‘working in the garden’. In the same way, the verb phrase ‘will be vacationing in Mexico’ contains the smaller verb phrase ‘vacationing in Mexico’.
The predicate of an English sentence is always a verb phrase. Verb phrases can also occur in non-predicate positions.
In the sentence, ‘Having finished her work, Susie went home’, the sequence ‘having finished her work’ is an example of a verb phrase, but it is not in the predicate position.