Abstract: The reconstruction of non-uniformly sampled signal is needed very frequently in many applications in several diverse areas.The strengths of traditional Fourier reconstruction with minimum norm (FRMN) algorithm are that it is theoretically straightforward, and requires few assumptions.However, it is can not be used for sparse reconstruction.This paper proposes a novel Fourier reconstruction with variable sparseness (FRVS) algorithm.And the algorithm's probability interpretation is given based on the Bayesian inference.By introducing sparse constrained matrix, the idea of sparse reconstruction is integrated into the FRVS.Moreover, the FRVS owns the same solving form as FRMN.Experiments on the reconstruction of 1D complex theoretic signal show that FRVS has higher reconstruction accuracy than FRMN.Finally, FRVS is applied to the reconstruction of practical electrocardiogram (ECG) signal.The results illustrate FRVS can solve practical reconstruction problem, and it is necessary to select suitable sparseness parameter in the reconstruction.