At close of play McCullum was 109 not out off just 122 balls, with Taylor unbeaten on 103. Hamish Rutherford (62) and Peter Fulton (61) earlier chipped in with half centuries on a dispiriting day for the tourists.
New Zealand lost the toss but quickly made the West Indies attack look ordinary despite a green-tinged wicket and cloud cover for much of the day.
New Zealand's senior batsmen added a further 173 runs in the final session, heaping more misery on the tired West Indies attack,ending the day with an unbeaten partnership worth 182.
Captain McCullum, who made no secret of his wish to bowl first, was at his aggressive best, bringing up the 300 with a mighty six when he pulled Shannon Gabriel over square leg.
The innings was a personal boost for McCullum, who has been suffering from a severe back injury that requires him to use painkillers to take the field.
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