Correlation filters (CFs) have been applied to visual tracking with success providing excellent performance in terms of accuracy and efficiency. The underlying periodic assumption of the training samples results in their great efficiency when using the fast Fourier transform (FFT), yet it also brings unwanted boundary effects. To address this issue, the recently proposed spatially-regularized discriminative CF (SRDCF) method introduces a Gaussian weight function to regularize the learning filter, yielding favorable performances in accuracy but high computational complexity because the objective of the SRDCF cannot achieve a closed solution via the FFT. Motivated by SRDCF, we present an efficient and effective CF-based tracker using center-biased constraint weights (CBCWs), which improve simultaneously speed and accuracy. Specifically, we first construct a CBCW function by exploiting the symmetry of the Fourier transform. The values of the constraint weights are real in both time and frequency domains, so that the optimization can be directly solved in the frequency domain without any data transformation, thereby greatly reducing its computational complexity. Moreover, according to the average peak-tocorrelation energy value of the CF response, we propose an efficient and effective filter update strategy to handle occlusions during tracking. Extensive experiments on the OTB-2013, OTB- 2015, and VOT2016 benchmarks demonstrate that the proposed tracker significantly outperforms the baseline SRDCF in terms of accuracy and efficiency. Moreover, the proposed method performs favorably against 16 other representative state-of-the-art methods regarding robustness and success rate.