We have analyzed heat and mass transfer characteristics of Maxwell nanofluid flow over a vertical cone filled with carbon nanotubes by taking velocity and thermal slip effects into the account in this analysis. The appropriate similarity variables are introduced to convert partial differential equations into the system of ordinary differential equations. The most suitable Finite element analysis is used to solve these equations together with boundary conditions. The variations in velocity, temperature and concentration distributions for various values of pertinent parameters, such as, Magnetic parameter (0.5-1.5), Volume fraction parameter (0.05-0.3), Buoyancy ratio parameter (0.1-0.7), Maxwell parameter (0.0-1.2), Radiation parameter (0.1-0.4), Prandtl number (4.2-7.2), Chemical reaction parameter (0.1-0.7), Velocity slip parameter (0.1-0.8), thermal slip parameter (0.5-1.5) are calculated and results are plotted through graphs. Furthermore, the velocity, heat and mass transfer rates are also calculated and are shown in tabular form. Comparison of present numerical code with existing results is made and found good agreement. It is noticed that temperature of the fluid elevates with rising values of nanoparticle fraction parameter and this rise is more in SWCNTs- water based nanofluid than the MWCNTs-water based nanofluid. It is also noticed that the rates of heat transfer elevates in MWCNTs - water based nanofluid, however, it retards in SWCNTs- water based nanofluid as the values of Maxwell parameter rises. (C) 2018 Elsevier B.V. All rights reserved.