The BL Lac object H1426+428 (z ≡ 0.129) is an established source of TeV γ-rays and detections of these photons from this object also have important implications for estimating the extragalactic background light in addition to the understanding of the particle acceleration and γ-ray production mechanisms in the AGN jets. We have observed this source for about 244 h in 2004, 2006 and 2007 with the TACTIC γ-ray telescope located at Mt Abu, India. Detailed analysis of these data do not indicate the presence of any statistically significant TeV γ-ray signal from the source direction. Accordingly, we have placed an upper limit of ≤1.18 × 10⁻¹² photons cm⁻² s⁻¹ on the integrated γ-ray flux at 3σ significance level.