This study discusses and explains behavioural and psychological factors influencing decision-making under uncertainty, i.e. outcome of the decision is uncertain as in insurance purchasing. The contributions of this study to insurance purchase decisionmaking are two-folds. First, it contributes to improve insurance companies understanding on their customers' decision-making behaviours and biases. Therefore, they can better market their products. Second, it contributes to improve insurance buyers understanding on decision-making biases influencing their judgement when they make decision under uncertainty. Therefore, they can make better decision when purchasing insurance products and the amount of coverage. Insurance purchase decision is complex and difficult. The complexities arise from issues such as evaluating the likelihood and magnitude of risks, assessing financial needs and choosing an insurance package. The difficulties arise because insurance buyers face difficulties to predict the likelihood and magnitude of highly unlikely and largely unfamiliar future events. The buyers also face difficulties in understanding risks. They fail in properly evaluate the extent, frequency and probabilities of risks, and in interpreting them correctly. They also face difficulties in choosing and evaluating insurance price, quality, and benefits, and in comparing different insurance products provided in the market. Studies have shown that insurance purchase decision is influenced by emotions such as affection, love, fear and anxiety. The emotions created decision-making biases. The biases can be the result of cognitive limitations, information processing and perception, problem organizing and cognitive styles. This study groups decision-making biases influencing insurance purchase decision in two: biases in heuristic judgement and decision framing. Detail explanation of both biases are given. The biases occur because of the interactions between the two human thinking systems, which is also discussed.