The Ghanaian banking system plays an important role in the development of a country’s economy and its financial stability by acting as an intermediary between depositors who have excess funds and borrowers who are in need of funds. In recent times banks have become cautious in extending advances as a result of the rise in non-performing assets. A non-performing asset (NPA) is a debt obligation where the borrower has not paid any previously agreed upon interest and principal repayments to the designated lender for a period beyond 90 days thus not yielding any income to the lender in the form of principal and interest payments. The study employed quantitative research design with secondary data for the period 2008-2017. An attempt was made to study the trend of total advances, net profit, Gross Non-Performing Asset and Net Non-Performing Asset of GCB Bank Limited and Standard Chartered Bank Ghana Limited. The results showed a general increasing trend of Total advances, Gross Non-Performing Asset and Net Non-Performing Asset for both banks over the past 10 years. In addition, there was a positive relationship between the Net profit and Non-Performing Asset of GCB Bank Limited whilst a negative relationship existed between the Net profit and Non-Performing Asset of Standard Chartered Bank Ghana Limited.