As-75-zero-field nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) measurements are performed on CaFe2As2 under pressure. At P=4.7 and 10.8 kbar, the temperature dependence of nuclear-spin-lattice relaxation rate (1/T-1) measured at tetragonal phase show no coherence peak just below T-c and decrease with decreasing temperature. The superconductivity is of gapless at P=4.7 kbar but evolves to multiple gaps at P=10.8 kbar. We find that the superconductivity appears near a quantum critical point. Both electron correlation and superconductivity disappear in the collapsed tetragonal phase. A systematic study under pressure indicates that electron correlations play a vital role in forming Cooper pairs in this compound. (C) 2010 Elsevier Ltd. All rights reserved.