A continuous deformation descent direction method is proposed for approximating a solution of the linearly constrained concave quadratic minimization problem with simple bounds. The method consists of two major steps. One step is to update Lagrange multipliers with a globally and superliearly convergent iterative procedure. The other step is to generate a point in a descent direction, which is superior to the gradient descent direction and has a desired property that the simple bounds are satisfied automatically if the step length is a number between zero and one. Numerical results show that the method seems effective and efficient.