In CST, while designing the antenna, the antenna parameters return loss and VSWR is good. But the gain and directivity is not attaining as expected level. How to improve this??
What gain are you obtaining and what gain do you expect?
The maximum gain of the antenna is fundamentally limited by its electrical dimensions (proportional to the geometrical dimensions / operation wavelength) by the formula G/(4 pi) = A_phys * efficiency / wavelength^2.
You can find an explanation here https://en.wikipedia.org/wiki/Antenna_aperture
If your material losses are low or cannot be changed, then you need to increase the size of the antenna in some efficient manner. The simplest solution I would suggest is to do a 2 element array, i.e. a simple symmetrical power divider with one antenna at each of its outputs. You can see an example here:
Article Efficient Deformable Patch Antenna Design for Wearable Applications
By doubling the number of elements from 1 to 2, you should have around 3 dB more gain. More advanced designs are 4 element arrays in a linear array (4x1) or a 2-dimensional array (2x2). Also the use of metamaterials/near-zero materials can help, but all these solutions depend on the gain you expect and the limitations you face in terms of dimensions and technology.
Several approaches can be tried like parasitic patches, incorporation of slots of a particular shaped, EBG structure, meta-material, adding reflecting surface etc.
Although almost all of the options have been suggested by the learned colleagues, but the simplest method is to increase the width of patch.
Use low dielectric constant as suggested by others and increase the width of patch, this will reduce the beamwidth in E-plane and increase gain. Keeping in mind the complexity of fabrication, I find this method the simplest.
Also you may place passive metal patches or Metamaterial unit cells around the patch in order to improve Gain.
I have worked and proved that the latter method is almost as effective as placing a Zero/negative index material slab above the patch. This method reduces the design complexities. You may have a look at my publications for that.