The NZGeoid09 gravimetric quasigeoid model of New Zealand was computed through FFT-based Stokesian integration with a deterministically modified kernel and an iterative computation approach that accounts for offsets among New Zealand's 13 different local vertical datums (LVDs). NZGeoid09 is an improvement over the previous NZGeoid05 due to use of the EGM2008 and DNSC08GRA models, and due to improvements to the data processing strategy. The integration parameters of degree of kernel modification L = 40 and cap radius ψ0=2. 5° were determined empirically through a comparison with 1422 GPS/levelling observations, after the LVD offsets had been removed. The precision of NZGeoid09 was assessed using the same GPS/levelling dataset, yielding an overall standard deviation of 6.2 cm. NZGeoid09 performs better than NZGeoid05 and marginally better than EGM2008, but few data are available in the Southern Alps of New Zealand to give a better evaluation.