This paper presents an improved method for the prediction of the critical Reynolds number Recr for the secondary wake instability of flow past a circular cylinder based on three-dimensional (3D) direct numerical simulations (DNS). It is also found that insufficient mesh resolution in the plane perpendicular to the cylinder axis is a major cause for the over-prediction of Recr (∼ 200) reported in the literature using 3D DNS. It is demonstrated that the use of an optimized computational domain and mesh resolution (10 spanwise mesh layers to resolve only a half of a pair of the 3D mode) can reduce the computational cost significantly and yet retain adequate accuracy. The most accurate Recr predicted by the present DNS reduces to 190.74, which is consistent with independent linear stability analysis results of Recr ∼ 190. It is also demonstrated that 3D DNS is capable of accurately predicting the neutral curve for the secondary wake instability with a reasonable computational cost. The general conclusions drawn through a circular cylinder are expected to provide guidance on the prediction of Recr and neutral instability curve for other cylindrical objects.