Ni-rich NiTi alloys have been investigated by means of PAL spectroscopy, electrical resistivity measurement, 2D-ACAR and first principle calculation. An anomaly of positron lifetime has been observed for Ni(52)Ti(48) alloy which does not exhibit the martensitic transformation: positron lifetime increases by about 25 % with lowering temperature. Almost the same change in positron lifetime is observed on the subsequent heating run with little hysteresis. The 2D-ACAR for the same alloy also depends on temperature anomalously: the peak height of the 2D-ACAR increases by 20 % and the anisotropy decreases by 60 % with lowering temperature. Experimental results are discussed with the idea of Fermi surface nesting of B2-NiTi which has been evaluated from the 2D-ACAR spectra by LCW theory.