Dendrite formation on the anode surface of a battery is closely related to the safety and capacity of high energy density batteries, thus suppressing dendrite growth will significantly improve the performance of batteries. Many experimental reports reveal that convection near the dendrite nucleation site can change the local mass transport, and ultimately affect dendrite growth. Investigation of the convection effect in batteries will guide the development of strategies to suppress dendrite growth in a convective electrolyte. Most of the existing electro-convection computational models for dendrite growth studies are based on Eulerian frameworks. These methods have difficulty modeling the moving boundaries associated with dendrite growth and are less computationally efficient in simulating convective fluid motion. In this paper we adopt a mesh-free particle based Lagrangian method to address the challenges of previous grid based Eulerian electro-convection models. The developed model is verified by comparison to analytical solutions, including verification of ion migration and the electric potential. Simulation results show that the predicted dendrite growth and electro-convective flow patterns compare well with experimental results during early dendrite growth stages. Parametric studies reveal that low viscosity electrolytes suppress the dendrite growth by increasing the mass transport of ions near the anode/electrolyte interface.