Matrix　factorization　with　non-negative　constrains　is　widely　used　in　hyperspectral　image　fusion.　Nevertheless,　the　non-negative　restriction　on　the　sparse　coefficients　limits　the　efficiency　of　dictionary　representation.　To　solve　this　problem,　a　new　hyperspectral　image　fusion　method　based　on　non-factorization　sparse　representation　and　error　matrix　estimation　is　proposed　in　this　paper,　for　the　fusion　of　remotely　sensed　high-spatial　multi-bands　image　with　low-spatial　hyperspectral　image　in　the　same　scene.　Firstly,　an　efficient　spectral　dictionary　learning　method　is　specifically　adopted　for　the　construction　of　the　spectral　dictionary,　which　avoids　the　procedure　of　matrix　factorization.　Then,　the　sparse　codes　of　the　high-spatial　multi-bands　image　with　respect　to　the　learned　spectral　dictionary　are　estimated　using　the　alternating　direction　method　of　multipliers　(ADMM)　without　non-negative　constrains.　For　improving　the　quality　of　final　fusion　result,　an　error　matrix　estimation　method　is　also　proposed,　exploiting　the　spatial　structure　information　after　non-factorization　sparse　representation.　Experimental　results　both　on　simulated　and　real　datasets　demonstrate　that,　compared　with　the　related　state-of-the-art　methods,　our　proposed　method　achieves　the　highest　quality　of　hyperspectral　image　fusion,　which　can　improve　PSNR　over　2.5844　and　SAM　over　0.3758.