  We construct two interpolating solutions in type II string theory which
interpolate between an AdS$_5$ in the UV and a hyperscaling violating three
(spatial) dimensional Lifshitz space-time in the IR. The first solution is
non-supersymmetric and is obtained from a known intersecting non-supersymmetric
D3-brane with chargeless D0-brane solution of type IIB string theory, by
restricting some parameters characterizing the solution and going to a new
coordinate. In the IR the dilaton is non-constant in general and the metric is
three (spatial) dimensional hyperscaling violating Lifshitz with dynamical
critical exponent $z=(3+3\gamma)/(3-\gamma)$ and hyperscaling violation
exponent $\theta = 12/(3-\gamma)$, where $\gamma$ is a real parameter and can
take continuous values from $-1$ to $+1$. At the two extreme values, i.e., for
$\gamma = \pm 1$, the dilaton is constant. The second solution is
supersymmetric and is obtained from the known F-D2 bound state solution of type
IIA 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 AdS$_5$, whereas in the
IR, it gives a three dimensional hyperscaling violating Lifshitz with $z=3$ and
$\theta=2=d-1$.
