The ferromagnetic (FM) quantum critical system YbNi4P2 has been investigated by means of 31P-NMR. This is a newly discovered heavy fermion system which shows a FM transition at a very low TC=170mK. The present reported result is the extension of our previous work published in Ref. 11. 31P NMR results suggest the validity of the Korringa law in the presence of strong FM correlations. 31P NMR spectra have shown the anisotropic nature. The local magnetization derived from our NMR spectra is presented as a function of field at selected temperatures. The obtained spin-lattice relaxation rate 31(1/T1T) follows a weak power-law as T-0.75 in a wide field range down to T=1.8K. Possible scenarios for this unusual power-law behavior are discussed. Additionally, 31(1/T1T) is nicely scaled with the observed (C/T)2~T-0.8 power law in the temperature range 1.8-10K within the framework of renormalized Landau Fermi Liquid theory. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.