This study introduce a new frequency parameter called tau_{text{fcwt}}, which can be used to estimate earthquake magnitude on the basis of the first few seconds of P-waves, using the waveforms of earthquakes occurring in Japan. This new parameter is introduced using continuous wavelet transform as a tool for extracting the frequency contents carried by the first few seconds of P-wave. The empirical relationship between the logarithm of tau_{text{fcwt}} within the initial 4 s of a waveform and magnitude was obtained. To evaluate the precision of tau_{text{fcwt}}, we also calculated parameters tau_{text{p}}^{ hbox{max} } and tau_{text{c}}. The average absolute values of observed and estimated magnitude differences (|M_{text{est}} - M_{text{obs}} |) were 0.43, 0.49, and 0.66 units of magnitude, as determined using tau_{text{p}}^{ hbox{max} }, tau_{text{c}}, and tau_{text{fcwt}}, respectively. For earthquakes with magnitudes greater than 6, these values were 0.34, 0.56, and 0.44 units of magnitude, as derived using tau_{text{p}}^{ hbox{max} }, tau_{text{c}}, and tau_{text{fcwt}}, respectively. The tau_{text{fcwt}} parameter exhibited more precision in determining the magnitude of moderate- and small-scale earthquakes than did the tau_{text{c}}-based approach. For a general range of magnitudes, however, the tau_{text{p}}^{ hbox{max} }-based method showed more acceptable precision than did the other two parameters.