A　sequential　quadratic　programming　(SQP)　algorithm　is　presented　for　solving　nonlinear　optimization　with　overdetermined　constraints.　In　each　iteration,　the　quadratic　programming　(QP)　subproblem　is　always　feasible　even　if　the　gradients　of　constraints　are　always　linearly　dependent　and　the　overdetermined　constraints　may　be　inconsistent.　The　ℓ2　exact　penalty　function　is　selected　as　the　merit　function.　Under　suitable　assumptions　on　gradients　of　constraints,　we　prove　that　the　algorithm　will　terminate　at　an　approximate　KKT　point　of　the　problem,　or　there　is　a　limit　point　which　is　either　a　point　satisfying　the　overdetermined　system　of　equations　or　a　stationary　point　for　minimizing　the　ℓ2　norm　of　the　residual　of　the　overdetermined　system　of　equations.