The 33-year-old made his Test debut against England in Dunedin in March and went on to play in all three drawn Tests of the series.
Martin has said that he is hoping to taste victory in the forthcoming two-match series.
"It's very exciting, at 33 years old it's just wonderful to be playing Test cricket," Sky Sports News quotes Martin as saying.
"This is the highest moment yet for me. Every game seems to be another high at the moment and I'm just relishing every chance I get. Getting the chance to play at somewhere like Lord's and against an England side ranked number two in the world is wonderful.
"If everyone does their job and plays well I think we can beat anyone in the world. A draw was nice but we want to do the full job this time. Hopefully we can knock them over this time."
The first Test between England and New Zealand begins at Lord's on May 16.