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In this paper, we present a semi-proximal alternating direction method of multipliers (sPADMM) for solving 3-block separable convex minimization problems with the second block in the objective being a strongly convex function and one coupled linear equa-tion constraint. By choosing the semi-proximal terms properly, we establish the global convergence of the proposed sPADMM for the step-length τ ∈ (0, (1 + √5)/2) and the penalty parameter σ ∈ (0,+∞). In particular, if σ> 0 is smaller than a certain threshold and the first and third linear operators in the linear equation constraint are injective, then all the three added semi-proximal terms can be dropped and consequently, the convergent 3-block sPADMM reduces to the directly extended 3-block ADMM with τ ∈ (0, (1 +√5)/2)