This paper considers coordinated linear precoding in downlink multicell multiuser orthogonal frequency-division multiple access (OFDMA) network. A less-complex, fast and provably convergent algorithm that maximizes the weighted sum-rate with per base station (BS) transmit power constraint is formulated. We approximate the nonconvex weighted sum- rate maximization (WSRM) problem with a solvable convex form by means of sequential parametric convex approximation (SPCA) approach. The second order cone program (SOCP) formulations of the objective function and constraints of the optimization problem are derived through proper change of vari- ables, first order linear approximation and hyperbolic constraints transformation, etc. The algorithm converges to the suboptimal solution taking fewer number of iterations in comparison to other known iterative WSRM algorithms. Finally, numerical results are presented to justify the effectiveness and superiority of the proposed algorithm.