We have performed an isovalent substitution study in a layered titanium oxypnictide system BaTi$_{2}$(Sb$_{1-x}$Bi$_{x}$)$_{2}$O (0$leq xleq$ 0.40) by the measurements of x-ray diffraction, electrical resistivity and magnetic susceptibility. The parent compound BaTi$_{2}$Sb$_{2}$O is confirmed to exhibit superconductivity at 1.5 K as well as charge- or spin-density wave (CDW/SDW) ordering below 55 K. With the partial substitution of Sb by Bi, the lattice parameters $a$, $c$ and $c/a$ all increase monotonically, indicating negative chemical pressure and lattice distortion on the (super)conducting Ti$_2$Sb$_2$O-layers. The Bi doping elevates the superconducting transition temperature to its maximum $T_c$=3.7 K at $x=$0.17, and then $T_c$ decreases gradually with additional Bi doping. A metal-to-nonmetal transition takes place around $x$=0.3, and superconductivity at $sim$1K exists at the nonmetal side. The CDW/SDW anomaly, in comparison, is rapidly suppressed by the Bi doping, and vanishes for $xgeq$0.17. The results are discussed in terms of negative chemical pressure and disorder effect.
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