To alleviate the problem of large error in the parameter estimation of linear frequency modulation (LFM) signal with high chirp-rates by traditional algorithms, a parameter estimation algorithm of LFM signal was proposed based on a new discrete fractional Fourier transform (DFrFT). A new dimensional normalization method combined with scale transformation was introduced into the DFrFT on the basis of the traditional discrete algorithm, and its normalization factor could change adaptively with the change in the transformation order. Based on the proposed DFrFT, the mathematical model of the parameter estimation algorithm of LFM signal was established. First, the LFM signal to be estimated was preprocessed by the new dimensional normalization method. The signal was converted from time-frequency domain to two dimensionless domains, and then the signal was processed by DFrFT. Next, the resolution of chirp-rate parameter estimation in high chirp-rate band was improved using the scale transformation characteristics of the new dimensional normalization method, and the chirp-rate optimize-range of the parameter estimation algorithm was theoretically deduced in comparison with the traditional algorithm. Finally, the effectiveness of the proposed algorithm was simulated under different chirp-rates and signal-to-noise ratios, and the results were compared with those of the traditional algorithm. Simulation results show that when the chirp-rate of the signal to be estimated was high, the proposed dimensional normalization method could effectively improve the estimation accuracy of the chirp-rate, and the performance improvement was more obvious in the environment of high signal-to-noise ratio.