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Frequency modulation to amplitude modulation(FM-to-AM)conversion is important for controlling temporal shapes of high-power Nd:glass lasers in the application of fusion ignition.To suppress this FM-to-AM conversion effect in the process of broadband third-harmonic generation of Nd:glass laser, we report an efficient frequencytripling scheme based on mixing narrowband and broadband pulses.Numerical results show that the FM-to-AM conversion in frequency conversion process can be suppressed effectively.For a required third-harmonic bandwidth of 1 THz, the defined relative modulation a in pulse intensity is as large as 180% in the conventional baseline design, while it will be reduced to only about 20% by using our proposed scheme.