A high-strength free-cutting copper alloy comprising: 75.4 mass% to 78.0 mass% of Cu; 3.05 mass% to 3.55 mass% of Si; 0.05 mass% to 0.13 mass% of P; 0.005 mass% to 0.070 mass% of Pb; optionally one or more element(s) selected from the group consisting of 0.01 mass% to 0.07 mass% of Sb, 0.02 mass% to 0.07 mass% of As, and 0.005 mass% to 0.10 mass% of Bi, wherein a total content of Sb, As and Bi is 0.10 mass% or lower; and a balance including Zn and inevitable impurities including Al, Ni, Mg, Se, Te, Fe, Mn, Sn, Co, Ca, Zr, Cr, Ti, In, W, Mo, B, Ag, and rare earth elements, wherein a total amount of Fe, Mn, Co, and Cr as the inevitable impurities is lower than 0.08 mass%, a content of Sn present as inevitable impurity is 0.05 mass% or lower, a content of Al present as inevitable impurity is 0.05 mass% or lower, a total content of Sn and Al present as inevitable impurity is 0.06 mass% or lower, when a Cu content is represented by [Cu] mass%, a Si content is represented by [Si] mass%, a Pb content is represented by [Pb] mass%, and a P content is represented by mass%, the relations of 78.0 ≤ f 1 = Cu + 0.8 × Si + P + Pb ≤ 80.8 and 60.2 ≤ f 2 = Cu − 4.7 × Si − P + 0.5 × Pb ≤ 61.5 are satisfied, in constituent phases of metallographic structure, when an area ratio of α phase is represented by (α) %, an area ratio of β phase is represented by (β)%, an area ratio of γ phase is represented by (γ)%, an area ratio of κ phase is represented by (κ)%, and an area ratio of μ phase is represented by (μ) %, the relations of 29 ≤ κ ≤ 60, 0 ≤ γ ≤ 0.3, β = 0, 0 ≤ μ ≤ 1.0, 98.6 ≤ f 3 = α + κ, 99.7 ≤ f 4 = α + κ + γ + μ, 0 ≤ f 5 = γ + μ ≤ 1.2, and 30 ≤ f 6 = κ + 6 × γ 1 / 2 + 0.5 × μ ≤ 62 are satisfied, the length of the long side of γ phase is 25 μm or less, the length of the long side of μ phase is 20 μm or less, and acicular κ phase is present in α phase. 75.4 mass% to 78.0 mass% of Cu; 3.05 mass% to 3.55 mass% of Si; 0.05 mass% to 0.13 mass% of P; 0.005 mass% to 0.070 mass% of Pb; optionally one or more element(s) selected from the group consisting of 0.01 mass% to 0.07 mass% of Sb, 0.02 mass% to 0.07 mass% of As, and 0.005 mass% to 0.10 mass% of Bi, wherein a total content of Sb, As and Bi is 0.10 mass% or lower; and a balance including Zn and inevitable impurities including Al, Ni, Mg, Se, Te, Fe, Mn, Sn, Co, Ca, Zr, Cr, Ti, In, W, Mo, B, Ag, and rare earth elements, wherein a total amount of Fe, Mn, Co, and Cr as the inevitable impurities is lower than 0.08 mass%, a content of Sn present as inevitable impurity is 0.05 mass% or lower, a content of Al present as inevitable impurity is 0.05 mass% or lower, a total content of Sn and Al present as inevitable impurity is 0.06 mass% or lower, when a Cu content is represented by [Cu] mass%, a Si content is represented by [Si] mass%, a Pb content is represented by [Pb] mass%, and a P content is represented by mass%, the relations of 78.0 ≤ f 1 = Cu + 0.8 × Si + P + Pb ≤ 80.8 and 60.2 ≤ f 2 = Cu − 4.7 × Si − P + 0.5 × Pb ≤ 61.5 are satisfied, in constituent phases of metallographic structure, when an area ratio of α phase is represented by (α) %, an area ratio of β phase is represented by (β)%, an area ratio of γ phase is represented by (γ)%, an area ratio of κ phase is represented by (κ)%, and an area ratio of μ phase is represented by (μ) %, the relations of 29 ≤ κ ≤ 60, 0 ≤ γ ≤ 0.3, β = 0, 0 ≤ μ ≤ 1.0, 98.6 ≤ f 3 = α + κ, 99.7 ≤ f 4 = α + κ + γ + μ, 0 ≤ f 5 = γ + μ ≤ 1.2, and 30 ≤ f 6 = κ + 6 × γ 1 / 2 + 0.5 × μ ≤ 62 are satisfied, the length of the long side of γ phase is 25 μm or less, the length of the long side of μ phase is 20 μm or less, and acicular κ phase is present in α phase.