Can one say "I am closing my business" ? or how can one phrase it ?
The idiomatic phrase for this in American English would be "going out of business." For example, this article uses this term a number of times (also "went out of business" in the past tense), and many more examples can be found online.
A store might, for example, have a "going-out-of-business sale" to sell off all its assets. This process of selling off of all assets can also be more formally referred to as "liquidation"—converting all of the business's assets into cash.