We report here a high dielectric percolative polymer nanocomposite, fabricated by a combination of triethylene-tetramine (TETA) modified multiwalled carbon nanotube (named as TETA-MWNT) within epoxy resin matrix. In this composite system, with various TETA-MWNT volume fractions, the dielectric constant (K) is well fitted by the scaling law of the percolation theory with the percolation threshold f (c) is 0.042 and the critical exponent p is 0.786. At 1,000 Hz of room temperature, the value of the dielectric constant is as high as 421 with the TETA-MWNT content of 4.14vol%, which is almost 60 times higher than that of epoxy resin. In contrast, a simple blend of pristine MWNT in epoxy composite shows evident lower dielectric constant and much higher loss with the same volume fraction.