diff --git a/src/MOI_wrapper/MOI_wrapper.jl b/src/MOI_wrapper/MOI_wrapper.jl
index 4a97ea9..8961c0b 100644
--- a/src/MOI_wrapper/MOI_wrapper.jl
+++ b/src/MOI_wrapper/MOI_wrapper.jl
@@ -338,7 +338,7 @@ mutable struct Optimizer <: MOI.AbstractOptimizer
                 _INVERSE_HASH,
             )
         model.next_column = 1
-        model.last_constraint_index = 1
+        model.last_constraint_index = 0
         model.columns_deleted_since_last_update = Int[]
         model.affine_constraint_info = Dict{Int,_ConstraintInfo}()
         model.quadratic_constraint_info = Dict{Int,_ConstraintInfo}()
diff --git a/test/MOI/MOI_wrapper.jl b/test/MOI/MOI_wrapper.jl
index 0b18296..9bb0d59 100644
--- a/test/MOI/MOI_wrapper.jl
+++ b/test/MOI/MOI_wrapper.jl
@@ -870,6 +870,14 @@ function test_attribute_TimeLimitSec()
     return
 end
 
+function test_last_constraint_index()
+    model = Gurobi.Optimizer(GRB_ENV)
+    x = MOI.add_variable(model)
+    c = MOI.add_constraint(model, 1.0 * x, MOI.GreaterThan(1.0))
+    @test c.value == 1
+    return
+end
+
 end
 
 TestMOIWrapper.runtests()