This study set out to investigate the effect of anisotropy on the Λ CDM model in the framework of Brans−Dicke theory. To this end, astrophysical constraints on this model using current available data including type Ia supernovae (SNIa), the Baryon Acoustic Oscillation (BAO), and the Hubble parameter H (z) data were deployed. Here, we present combined results from these probes, deriving constraints on Ω σ 0 of Λ CDM model and its anisotropy energy density in an anisotropic universe. It is found that Ω σ 0 can be constrained by the SNIa + H (z) + BAO data, with the best fitting value Ω σ 0 = (− 6. 5 2 ± 4. 2 1) × 1 0 − 4 for the Brans–Dicke cosmology. We extend our study to the case of Λ CDM model in an anisotropic universe and Brans–Dicke framework and find out that the equation of state parameter ( ω Λ ) cannot cross the phantom line and eventually the universe approaches a quintessence era. [ABSTRACT FROM AUTHOR]