Abstract: Quadric time-frequency distribution can reveal the characteristic of signals by means of the combination of the features of time and frequency domains. A new time-frequency distribution was proposed by designing a new kernel function with a narrow time domain and a wide frequency domain and concentration of energy in low frequencies. The new time-frequency distribution has great power in analyzing various complex signals. An example is presented to show that the distribution has a high resolution in both time and frequency domains, and can reveal cyclic weak pulse components merged in the strong background of resonance noises and harmonic components. Such a distribution is a power tool for the diagnosis of mechanical faults.