We consider the risk-minimizing hedging problem for unit-linked life insurance in a financial market driven by a shot-noise process. Because the financial market is incomplete, the insurance claims cannot be hedged completely by trading stocks and bonds only, leaving some risk to the insurer. The theory of ((pseudo) locally) risk-minimization is applied after a change of measure. Then the risk-minimizing trading strategies and the associated intrinsic risk processes are determined for two types of unit-linked contracts represented by the pure endowment and the term insurance. Copyright © 2009 John Wiley & Sons, Ltd.