We construct two interpolating solutions in type II string theory which interpolate between AdS5 in the UV and a hyperscaling-violating three (spatial)-dimensional Lifshitz spacetime in the IR. The first solution is nonsupersymmetric and is obtained from a known intersecting nonsupersymmetric D 3-brane with a chargeless DO-brane solution o f type IIB string theory, by restricting some para meters characterizing the solution and going to a new coordinate. In the IR the dilaton is nonconstant in general and the metric is three (spatial)-dimensional hyperscaling-violating Lifshitz spacetime with dynamical critical exponent z = (3 + 3y)/(3 -y) and hyperscaling-violation exponent 0 = 12/ ( 3 -y ) , where y is a real parameter and can take continuous values from -1 to + 1 . At the two extreme values, i.e., for y = ± 1 , the dilaton is constant. On physical grounds it is found that y m ust be restricted to lie in the range -1 < y < 0. The second solution is supersymmetric and is obtained from the known F-D2 bound-state solution o f type HA string theory by zooming into a particular region of space. In the UV, the proper description is given in a T-dual frame which is AdS5, whereas in the IR, it gives a three-dimensional hyperscaling-violating Lifshitz spacetime with z = 3 and 0 = 2 = d -l.