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In this paper, we study minimal algebraic surfaces of general type with K 2 = 3 p g − 5. Since the case p g ≤ 4 has been studied by Horikawa, Zucconi, and Bauer, we always assume p g ≥ 5 here. We prove that for such a surface, the canonical map is generically finite of degree 1 or 2. If the degree of the canonical map is 2, then the canonical image is a ruled surface, moreover, for any fixed (p g ≥ 14 , K 2 = 3 p g − 5) , there exists such a regular surface. If the degree of the canonical map is 1, then the surface is regular (i.e. q = 0) and its canonical linear system is base point free or has one simple base point. In the case where the canonical map is birational and the canonical linear system is base point free, we study the property of its canonical image and prove that for any fixed (p g ≥ 5 , K 2 = 3 p g − 5) , there exists such a surface. [ABSTRACT FROM AUTHOR]