Electron-tunneling measurements on the new superconductor MgB2 with T-c = 39 K have been carried out using a break-junction technique. The measurements reveal the largest gap value of 2Delta = 17-19 meV at 4.2 K. This value leads to the ratio 2Delta/k(B)T(c) = 5-5.6, indicating the strong-coupling superconductivity. We have also observed the reproducible gap values of 2Delta congruent to 4-4.5 meV and 7-9 meV. The smallest gap exists even beyond 30 K. We will discuss the implication of the data. (C) 2002 Published by Elsevier Science B.V.