Simply connected closed symplectic 4-manifolds with b(2)(+) = 1 and K-2 = 0 are investigated. As a result, it is confirmed that most of homotopy elliptic surfaces {E(1)K \ K is a fibred knot in S-3} constructed by R. Fintushel and R. Stern in Invent. Math. 134 (1998) 363-400 are simply connected closed minimal symplectic 4-manifolds that do not admit a complex structure.