deformations, and charge radii of deformed nuclei quite well, the differences between the predicted binding energies and the corresponding data are somewhat large for spherical nuclei. Therefore, it is necessary to have a new parametrization for the nuclear covariant energy density functional with point-coupling interaction to describe both the nuclear matter and finite nuclei properties. In this work, a new parametrization PC-PK1 with nonlinear coupling interactions is proposed. In Sec. II, the theoretical framework for the relativistic point- coupling model is briefly outlined. The numerical details are given in Sec. III. In Sec. IV-VII, a series of illustrative descriptions for the nuclear matter, spherical nuclei, deformed nuclei as well as the nuclear excited properties are presented. Finally, a summary is given in Sec. VIII. The basic building blocks of RMF theory with point-coupling vertices are where ψ is Dirac spinor field of nucleon, ⃗ τ is the isospin Pauli matrix, and Γ generally denotes the 4 × 4 Dirac matrices. There are ten such building blocks characterized by their transformation characteristics in isospin and Minkowski space. In this paper, vectors in the isospin space are denoted by arrows and the space vectors by bold type. Greek indices µ and ν run over the Minkowski indices 0, 1, 2, and 3. A general effective Lagrangian can be written as a power series in ¯ ψ O Γ ψ and their derivatives. We start with the following Lagrangian density of the point-coupling model which is divided as the Lagrangian density for free nucleons L $^{free}$, the four-fermion point-coupling terms L $^{4f}$, II. THEORETICAL FRAMEWORK ( ¯ ψ O Γ ψ ) , O ∈ { 1 , ⃗ τ } , Γ ∈ { 1 , γ$_{µ}$, γ$_{5}$, γ$_{5}$γ$_{µ}$, σ$_{µν}$ } , (1) L = L free + L 4f + L hot + L der + L $^{em}$, (2) L free = ¯ ψ ( iγ$_{µ}$∂ µ − m ) ψ, (3) L 4f = − 1 2 α$_{S}$ ( ¯ ψψ )( ¯ ψψ ) − 1 2 α$_{V}$ ( ¯ ψγ$_{µ}$ψ )( ¯ ψγ $^{µ}$ψ ) − 1 2 α$_{T S}$ ( ¯ ψ⃗ τ ψ )( ¯ ψ⃗ τ ψ ) − 1 2 α$_{T V}$ ( ¯ ψ⃗ τ γ$_{µ}$ψ )( ¯ ψ⃗ τ γ $^{µ}$ψ ) , (4) 4