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.