The modified embedded atom method (MEAM) can describe the physical properties of bulk systems for a wide range of advanced engineering materials. However, the MEAM is found to return negative surface energy for Li(100), Li(110) and Li(111), if the relaxation of atomic positions on the surface is taken into account. In order to solve this problem, a new scheme of MEAM for lithium has been developed, by modifying the expression of embedding function. In this work, the new scheme is also applied to the other alkali metals, and the parameter sets of MEAM have been determined by fitting to not only bulk properties but also some non-bulk properties. The new MEAM potentials for alkali metals have been applied to calculate the elastic stiffness of crystal, the vacancy formation energy, the surface energies for low index crystal faces and the bond length and the binding energy for dimer. The results have been compared with experimental values.