Why are we searching for graviton? I am computer scientist and not a physicist, but I really like physics
One question popped into my mind recently about gravity. General theory of relativity describes gravity not as a force but as a curvature of space-time. So if gravity is not a force but just illusion caused by curvature of space-time then why do we consider it to be a fundamental force
And why are searching for force carrying particle for gravity if it is not a force?
 A: You have to be careful with the word "is" in physics.
In Newton's day, you could say "Gravity is an action at a distance between masses." Later on you would update this to "Gravity is a vector field similar to the electric field sourced by masses." Later on still, you might say something like in your question, that "gravity is the curvature of space-time."
In physics, we should really reserve the word "is" for observable quantities. "The temperature of so and so is such and such." Theoretical concepts and models provide a useful and necessary framework for us to reason about the physical world. But our theories are at best a faithful representation of Nature in some domain, we cannot say that they are Nature.
In this vein, GR provides a very useful and comprehensive framework to understand gravity in a classical (non-quantum) regime, with dense objects moving at large speeds compared to the speed of light, or for large gravitational fields. However, this representation most likely breaks down when we consider quantum effects.
On the other hand, we have the framework of perturbative quantum gravity, where the metric is approximately flat Minkowski space, with no gravity, plus a very small perturbation away from flat space describing the gravitational field. This description is valid only for weak gravitational fields, but it has many mathematical similarities to other theories of particle physics. Therefore, in this representation, within its regime of validity, we can proceed as a particle physicist and treat the metric perturbation quantum mechanically, leading to gravitons.
What we would ultimately like is some deeper theory, which is valid both for strong gravitational fields and that is quantum mechanical. It should reduce to GR in the strong field, classical regime, and should reduce to perturbative quantum gravity in the quantum, weak field regime. (At least, that is the naive expectation, although people have tried lots of ways to develop this missing theory that don't fit this naive pattern). We don't really know what this theory is. String theory is an example of a theory which has this behavior, but we don't know if it really describes nature or not (beyond the regimes where it reduces to other, previously known theories of physics).
Having said all of that, experimental prospects for ever being able to directly detect a graviton, even in principle are quite grim. There is a delightful essay by Dyson where he argues that an attempt to build a LIGO-type device to detect a graviton will necessarily collapse into a black hole before it is sensitive enough to detect one. https://publications.ias.edu/sites/default/files/poincare2012.pdf
