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This study analyzes the relationship between bank efficiency and liquidity risks of 16 Islamic banks and 27 conventional banks in Malaysia for the period covering year 1994-2014. Bank efficiency is based on cost efficiency, while liquidity risk is measured based on the guidelines of Basel III using Liquidity Coverage Ratio (LCR), which is short term (30 days) and Net Stable Funding Ratio (NSFR), which is long term (one year) in nature. This analysis involves two phases: 1) the cost efficiency scores is estimated using Stochastic Frontier Analysis (SFA) and 2) the relationship between the estimated cost efficiency and liquidity risk is tested using static panel regression method. The results show that cost efficiency of both banking systems have no significant relationship with LCR, but significant negative relationships with NSFR for both Islamic and conventional banks. This means that the higher the cost inefficiency, the lower is the liquidity, and the higher the liquidity risk in long term. In short, cost saving can reduce bank liquidity risk in long-term. Hence, bank cost efficiency must be taken into account by policymakers in formulating liquidity risk management to ensure sustainability of the banking system in Malaysia. [ABSTRACT FROM AUTHOR]