Management of risk by a pest in agriculture is one of the major concerns of the decision makers and policy planners. There is always risk of introduction of alien weed seeds along with the imported cereals. This study revealed that how much cost may be involved in management of an alien introduced weed in due course mentioning example of Parthenium which got introduced into India in 1955 along with imported cereals. Initially Parthenium was a problem in waste and vacant land. Reports started to appear about its infestation in field crops after 1980. In general, about 35 million hectare land has been estimated to be infested with Parthenium currently. The increase of Parthenium infestation in crop area in recent past is alarming. For the management of Parthenium, two hand weeding or two chemical sprays are essentially required to get complete relief. It was estimated that 182000 or 18200 crores will be required per year to mitigate the problem by manual labour and Rs 119000 million or 11900 crores are required to manage the weed by Chemical method besides Rs 880 crores for treatment of health and about 10 crores on researchable issues related to biological control in particular and integrated management in general including people awareness programmes. Therefore, since 1955, it would have cost Rs 2067160 million or 206716 crores to manage the parthenium in India by manual labour The losses caused by this weed may be much higher if we take into consideration the cost involved in restoration of biodiversity and aesthetic value already lost due to Parthenium