A good way to strengthen your peripheral vision is to cover up your foveal or central vision and use your peripheral vision only. Thus it will force yourself to rely on your peripheral vision. This will increase in sensitivity and range of your peripheral vision in the future.
Here is one method I find on Internet which is quite useful to improve peripheral vision. You can have a try.
1.Place your hands together in front of you as when praying or greeting in the Indian fashion (namaste). Now, separate your hands by about an inch. You will begin to see a third palm between the two real palms.
2.Bring the index fingers of your two hands together facing each other so that the tips of the fingers tough. Now separate the two fingers apart by about an inch. You will begin to see a third finger in the middle.