Abstract: This paper extends the quadratic consistent 1-point (QC1) integration method to the meshfree analysis of heat conduction. The discretized equation for the problem and the equation to correct the derivatives at quadrature points are given. Numerical results show that: in the comparison to the standard triangle integration method and the existing 1-point integration method which only satisfies the linear consistency, the proposed QC1 method can pass the quadratic patch test exactly and exhibits better accuracy, convergence and computational efficiency for both the static and transient heat conduction.