  The Weakly Interacting Massive Particles(WIMPs) have long been the favored
CDM candidate in the standard $\Lambda$CDM model. However, owing to great
improvement in the experimental sensitivity in the past decade, some parameter
space of the SUSY-based WIMP model is ruled out. In addition, WIMP as the CDM
particle is also at variance with other astrophysical observables at small
scales. We consider a model that addresses both these issues. In the model, the
WIMP decays into a massive particle and radiation. We study the background
evolution and the first order perturbation theory (coupled Einstein-Boltzmann
equations) for this model and show that the dynamics can be captured by a
single parameter $r=m_L/q$, which is the ratio of the lighter mass and the
comoving momentum of the decay particle. We incorporate the relevant equations
in the existing Boltzmann code CLASS to compute the matter power spectra and
CMB angular power spectra. The decaying WIMP model is akin to a non-thermal
Warm Dark Matter(WDM) model and suppresses matter power at small scales, which
could alleviate several issues that plague the CDM model. We compare the
predictions of the model with CMB, galaxy clustering, and high-z HI data. Both
these data sets yield $r\gtrsim 10^6$, which can be translated into the bounds
on other parameters. In particular, we obtain the following lower bounds on the
thermally-averaged self-annihilation cross-section of WIMPs $\langle \sigma v
\rangle$, and the lighter mass $m_L$: $\langle \sigma v \rangle \gtrsim
4.9\times 10^{-34} \, \rm cm^3 \, sec^{-1}$ and $m_L \gtrsim 2.4 \, \rm keV$.
The lower limit on $m_L$ is comparable to constraints on the mass of
thermally-produced WDM particle. The limit on the self-annihilation
cross-section greatly expands the available parameter space as compared to the
stable WIMP scenario.
