Abstract: Strain engineering is an effective way to tune the intrinsic properties of a material. Here, we show by using first-principles calculations that both uniaxial and biaxial tensile strain applied to monolayer TiS3 are able to significantly modify its intrinsic mobility. From the elastic modulus and the phonon dispersion relation we determine the tensile strain range where structure dynamical stability of the monolayer is guaranteed. Within this region, we find more than one order of enhancement of the acoustic phonon limited mobility at 300 K (100 K), i.e. from 1.71 x 10(4) (5.13 x 10(4)) cm(2) V-1 s(-1) to 5.53 x 10(6) (1.66 x 10(6)) cm(2) V-1 s(-1). The degree of anisotropy in both mobility and effective mass can be tuned by using tensile strain. Furthermore, we can either increase or decrease the band gap of TiS3 monolayer by applying strain along different crystal directions. This property allows us to use TiS3 not only in electronic but also in optical applications.