Selective laser melting is a laser based additive manufacturing process in which both melting and solidification play essential roles. In this paper, we present a numerical model for simultaneous melting and micro-scale solidification of a binary alloy sample during the laser melting process. The model is developed by making appropriate modifications to the governing equations of momentum, energy and species conservation based on the well-known enthalpy method. The effect of the fixed laser source is incorporated as a heat flux term at the top surface. Natural convection and Marangoni convection are implemented in the model. Powder effect is considered by effective thermal conductivity which is defined as a function of the porosity of the powder bed. This paper mainly emphasises the dendrite growth and microsegregation in binary alloys during a laser melting process.