Latest observational reports of solar flares reveal some uncommon features of microwave spectra, such as unusually hard (or even positive) spectra, and/or a super-high peak frequency. For a better understanding of these features, we conduct a parameter study to investigate the effect of brokenpower-law spectra of energetic electrons on microwave emission on the basis of gyrosynchrotron mechanism. The electron broken-power-law energy distribution is characterized by three parameters, the break energy (E B ), the power-law indices below (δ 1 ) and above (δ 2 ) the break energy. We find that with the addition of the δ 2 component of the electron spectra, the total flux density can increase by several times in the optically-thick regime, and by orders of magnitude in the optically-thin regime; the peak frequency (ν p ) also increases and can reach up to tens of GHz; and the degree of polarization (r c ) decreases in general. We also find that (1) the variation of the flux density is much larger in the optically-thin regime, and the microwave spectra around the peak frequency manifest various profiles with the softening or soft-hard pattern; (2) the parameters δ 1 and E B affect the microwave spectral index (α) and the degree of polarization (r c ) mainly in the optically-thick regime, while δ 2 mainly affects the optically-thin regime. The results are helpful in understanding the lately-reported microwave bursts with unusual spectral features and point out the demands for a more-complete spectral coverage of microwave bursts, especially, in the high-frequency regime, say, > 10 − 20 GHz.