We report synthesis of Co substitution at Fe site in Fe1-xCoxSe0.5Te0.5 (x=0.0 to 0.10) single crystals via vacuum shield solid state reaction route using flux free method. Single crystal XRD results showed that these crystals grow in (00l) plane i.e., orientation in c-direction. All the crystals possess tetragonal structure having P4/nmm space group. Detailed scanning electron microscopy (SEM) images show that the crystals are grown in slab-like morphology. The EDAX results revealed the final elemental composition to be near stoichiometric. Powder X-Ray diffraction (PXRD) Rietveld analysis results show that (00l) peaks are shifted towards higher angle with increasing Co concentration. Both a and c lattice parameters decrease with increasing Co concentration in Fe1-xCoxSe0.5Te0.5 (x=0.0 to 0.10) single crystals. Low temperature transport and magnetic measurements show that the superconducting transition temperature (Tc), decreases from around 12K to 10K and 4K for x=0.03 and x=0.05 respectively. For x=0.10 crystal superconductivity is not observed down to 2K. Electrical resistivity measurement of Fe0.97Co0.03Se0.5Te0.5 single crystal under magnetic field up to 14Tesla for H//ab and H//c clearly showed the anisotropy nature of superconductivity in these crystals. The upper critical field Hc2(0), being calculated using conventional one band Werthamer–Helfand–Hohenberg (WHH) equation, for x=0.03 crystal comes around 70Tesla, 45Tesla and 35Tesla for normal state resistivity criterion ρn=90%, 50% and 10% criterion respectively for H//c and around 100Tesla, 75Tesla and 60Tesla respectively for H//ab. The activation energy of Fe0.97Co0.03Se0.5Te0.5 single crystal is calculated with the help of TAFF model for both H//c and H//ab direction. In conclusion, Co substitution at Fe site in Fe1-xCoxSe0.5Te0.5 suppresses superconductivity.