We have measured upper-critical-field H c2 , specific heat C, and tunneling spectra of the intermetallic perovskite superconductor MgCNi 3 with a superconducting transition temperature T c Ϸ7.6 K. Based on these measurements and relevant theoretical relations, we have evaluated various superconducting parameters for this material, including the thermodynamic critical field H c (0), coherence length (0), penetration depth (0), lower-critical-field H c1 (0), and Ginzburg-Landau parameter (0). From the specific heat, we obtain the Debye temperature ⌰ D Ϸ284 K. We find a jump of ⌬C/␥T c ϭ2.1 at T c ͑where ␥ is the normal-state electronic specific coefficient͒, which is larger than the weak-coupling BCS value of 1.43, suggesting that MgCNi 3 may be a strong-coupling superconductor. In addition, we observed a pronounced zero-bias conductance peak ͑ZBCP͒ in the tunneling spectra. We discuss the possible physical origins of the observed ZBCP.