Traditional statement coverage metric based on the activation of statements, without taking observability into account, can result in an artificially high reading of coverage and a false sense of confidence. So the observability-based statement coverage metric is proposed. This metric computes observability information to determine whether the effects of errors activated by the program stimuli can be observed. With the density and complexity of circuits extended, this metric plays a more and more important role during verification. Introduced in this paper is a method of vector generation for the observability-based statement coverage metric. The contribution of the work includes two aspects. Firstly, precise and concise abstract representations are presented from HDL descriptions to model observability information. Secondly, a novel simulation-based algorithm is presented to generate vectors for the observability-based statement coverage. During this procedure, the proposed algorithm always tries to cover all unobserved statements, and reduce unnecessary backtracking, so it is efficient. Finally, the method proposed has been implemented as a prototype tool for VHDL designs, and the results on benchmarks show the significant benefits.