Both are possible. In British English there is a subtle difference. 'I like taking photos' means that photography is something which you do, and which you enjoy doing. It's an activity which gives you pleasure. I presume that this is what you want to say. The second sentence suggests that it is something which you like in theory but which you don't necessarily do. It could also mean that you don't actually enjoy taking photos, but that you think that it is a good thing to do. For example, a car mechanic who repairs damaged cars might say 'I like to take photos of the cars before and after I repair them.' He doesn't enjoy taking these photos. It isn't fun, and it isn't his hobby, but he likes to have a record of his work in case a problem arises later. The second is more common in American English, and my impression is that American English does not make the same distinction.

I agree with Su.Ki. that American English does not make as much of a distinction between "I like taking photos" and "I like to take photos". In American English, both sentences communicate that the activity gives the speaker pleasure. The example of the car mechanic taking photos before and after repairing a car would also be used in American English. So, as Su.Ki. says, the verb "like" does not always signify pleasure; it can also signify preference.

Get in the habit of saying "I like taking photographs." This means something you already do. "To take" sounds as if you like the idea of it, but you don't do it often. Be careful of literally translating from your first language - yes, we understand what you mean, but you will often sound unnatural.

I like to take photograph is correct. ..because its your activity and taking is a action which shows you are doing