This transaction may take two forms: 

1 – Where the bank buys the goods for itself, then sells them to the customer after taking possession of them. This is what some Islamic banks do, and they call it a muraabahah transaction in which a letter of credit is opened in the interests of the customer. This is permissible, because if the bank buys the product for itself and takes possession of it, it is permissible for it to sell it for a higher price, to be paid immediately or in instalments. So it may buy it for one hundred, for example, and sell it for one hundred and ten in instalments. 

But in this case it is essential that the bank do the letter of credit in its own name, so that the product will in fact be bought by it, and it will not merely be a trick. 

2 – Where the role of the bank is to finance the purchase only, and not to buy the product for itself, rather t buys it for the customer in return for some profit or interest. This is a haraam, riba-based transaction, because in fact it is a loan with interest. The bank lends one hundred to the customer and takes back one hundred and ten. 

For more details please see al-Khadamaat al-Istithmaariyyah fi’l-Masaarif by Dr. Yoosuf al-Shubayli (2/470). 

And Allaah knows best.