Spectrum estimation is a popular method for identifying periodically expressed genes in microarray time series analysis. For unevenly sampled data, a common technique is applying the Lomb-Scargle algorithm. The performance of this method suffers from the effect of noise in the data. In this paper, we propose a new spectrum estimation algorithm for unevenly sampled data. The new method is based on signal reconstructing technic in aliased shift-invariant signal spaces and a direct spectrum estimation formula was derived based on B-spline basis. The new algorithm is very flexible and can reduce the effect of noise by adjusting the order of B-spline basis. The test on simulated noisy signal and typical periodically expressed gene data shows our algorithm is accurate compared with Lomb-Scargle algorithm