Machine Learning as a Service (MLaaS) is enabling a wide range of smart applications on end devices. However, privacy-preserved computation is still expensive. Our investigation has found that the most time-consuming component of the HE-based linear computation is a series of Permutation (Perm) operations that are imperative for dot product and convolution in privacy-preserved MLaaS. To this end, we propose GALA: Greedy computAtion for Linear Algebra in privacy-preserved neural networks, which views the HE-based linear computation as a series of Homomorphic Add, Mult and Perm operations and chooses the least expensive operation in each linear computation step to reduce the overall cost. GALA makes the following contributions: (1) It introduces a row-wise weight matrix encoding and combines the share generation that is needed for the GC-based nonlinear computation, to reduce the Perm operations for the dot product; (2) It designs a first-Add-second-Perm approach (named kernel grouping) to reduce Perm operations for convolution. As such, GALA efficiently reduces the cost for the HE-based linear computation, which is a critical building block in almost all of the recent frameworks for privacy-preserved neural networks, including GAZELLE (Usenix Security'18), DELPHI (Usenix Security'20), and CrypTFlow2 (CCS'20). With its deep optimization of the HE-based linear computation, GALA can be a plug-and-play module integrated into these systems to further boost their efficiency. Our experiments show that it achieves a significant speedup up to 700x for the dot product and 14x for the convolution computation under different data dimensions. Meanwhile, GALA demonstrates an encouraging runtime boost by 2.5x, 2.7x, 3.2x, 8.3x, 7.7x, and 7.5x over GAZELLE and 6.5x, 6x, 5.7x, 4.5x, 4.2x, and 4.1x over CrypTFlow2, on AlexNet, VGG, ResNet-18, ResNet-50, ResNet-101, and ResNet-152, respectively.