A new approach to the construction of efficient parallel solution methods of large sparse symmetric positive definite linear systems is considered. This approach is based on the variable block conjugate gradient (CG) method, a generalization of the block CG method. It is possible to reduce the iteration block size adaptively by construction of an \(A\)-orthogonal projector without restarts and without algebraic convergence of residual vectors. The approach allows to find the constructive compromise between the required resource of parallelism, the resulting convergence rate, and the serial operations count of one block iteration to minimize the total parallel solution time.