In　this　paper,　we　propose　the　hybrid-precoding　design　that　alleviates　the　performance　loss　caused　by　beam-misalignment　in　the　mmWave　multi-user　communication　systems.　To　this　end,　we　firstly　design　the　beam-misalignment　aware　fully-digital　precoders　for　two　distinct　scenarios.　First,　for　a　base-station　(BS)　with　full　estimated　channel-state-information　(CSI),　the　minimum-mean-squared-error　metric　incorporating　the　＇error-statistics＇　of　the　beam-misalignment　error　is　used　to　analytically　derive　a　closed-form　expression　for　the　fully-digital　precoder,　which　maximizes　the　array　gain　while　suppressing　the　inter-user　interference　for　each　user-equipment　(UE).　Second,　for　a　BS　which　can　only　acquire　partial　estimated　CSI,　a　min-max　non-convex　optimization　is　considered　to　obtain　the　fully-digital　precoder,　which　minimizes　the　maximum　loss　in　the　array　gains　of　the　expected　beam-misalignment　＇error-range＇　over　the　UEs　while　cancelling　the　inter-user　interference.　Subsequently,　we　propose　the　hybrid-precoding　design　that　approximates　the　fully-digital　designs　based　on　the　gradient-projection　method,　which　is　mathematically　proven　to　converge　to　an　approximate　local　solution　with　further　reduced　complexity　compared　to　the　state-of-the-art　algorithms.　Finally,　the　proposed　hybrid-precoding　design　is　further　extended　to　the　wideband　mmWave　communication　systems.　Numerical　results　show　that　the　proposed　hybrid-precoding　design　can　effectively　alleviate　the　performance　degradation　incurred　by　the　beam-misalignment.