DNA replication is a fundamental biological process during S phase of cell division. It is initiated from several hundreds of origins along whole chromosome with different firing efficiencies (or frequency of usage). Direct measurement of origin firing efficiency by techniques such as DNA combing are time-consuming and lack the ability to measure all origins. Recent genome-wide study of DNA replication approximated origin firing efficiency by indirectly measuring other quantities related to replication. However, these approximation methods do not reflect properties of origin firing and may lead to inappropriate estimations. In this paper, we develop a probabilistic model - Spanned Firing Time Model (SFTM) to characterize DNA replication process. The proposed model reflects current understandings about DNA replication. Origins in an individual cell may initiate replication randomly within a time window, but the population average exhibits a temporal program with some origins replicated early and the others late. By estimating DNA origin firing time and fork moving velocity from genome-wide time-course S-phase copy number variation data, we could estimate firing efficiency of all origins. The estimated firing efficiency is correlated well with the previous studies in fission and budding yeasts. The new probabilistic model enables sensitive identification of origins as well as genome-wide estimation of origin firing efficiency. We have successfully estimated firing efficiencies of all origins in S. cerevisiae, S. pombe and human chromosomes 21 and 22.