The application of queuing theory in the banking system, conducted a survey and analysis, from a technical point of view of what banks should take measures to make our customers the shortest waiting time, optimized system and improve efficiency. In this paper, a single channel queuing system with Poisson arrivals and exponential service and with queuing discipline of first come first serve basis is applied to arrivals and waiting times of customers in First Bank of Nigeria Plc, Ikotun branch, Lagos State, Nigeria. The queue size of customers including traffic intensity and average number of customers as well as the average time spent in the system and queue by a customer, are all obtained. The traffic intensity obtained is 0.8747 which indicate the probability of a customer queuing or waiting for service on arrival. The study concluded that more Automated Teller Machines (ATM) are needed by banks to reduce the time a customer will spend before he/ she is attended to; with this, more people will be interested in patronising banks thereby increasing efficiency and profitability.