All-electron calculations play an important role in density functional theory, in whichimproving computational efficiency is one of the most needed and challenging tasks.  In the model for-mulations, both the nonlinear eigenvalue problem and the total energy minimization problem pursueorthogonal solutions.  Most existing algorithms for solving these two models invoke orthogonalizationprocess either explicitly or implicitly in each iteration.  Their efficiency suffers from this process inview of its cubic complexity and low parallel scalability in terms of the number of electrons for largescale  systems.   To  break  through  this  bottleneck,  we  propose  an  orthogonalization-free  algorithmframework based on the total energy minimization problem.  It is shown that the desired orthog-onality can be gradually achieved without invoking orthogonalization in each iteration.  Moreover,this framework fully consists of BLAS operations and thus can be naturally parallelized.  The globalconvergence of the proposed algorithm is established.  We also present a preconditioning techniquewhich can dramatically accelerate the convergence of the algorithm.  The numerical experiments onall-electron calculations show the effectiveness and high scalability of the proposed algorithm.