Effective Lambda-nucleon interaction has been proposed in relativistic mean field approach based on nucleon-nucleon interaction PK1, by fitting single-lambda hypernuclei data along the hypernuclear chart. For a case of the omega-Lambda-Lambda tensor coupling is considered or not, meson sigma-, omega-Lambda couplings for Lambda-nucleon interaction are optimized to the experimental Lambda binding energy for hypernuclei [12-14]_LambdaC, [14,15]_LambdaN, [16]_LambdaO, [28]_LambdaSi, [32]_LambdaS, [40]_LambdaCa, [51]_LambdaV, [89]_LambdaY, [139]_LambdaLa and [208]_LambdaPb. These two independent hyperon-nucleon parameters are locally searched by a least-squares fit and later globally adjusted by a Levenberg-Marquardt minimization method while taking the obtained local minima as initial values. Hpernuclear properties, e.g., single particle energy, spin-orbit splitting of hyperon, from light to heavy mass region are presented. The results indicate that the newly developed interaction provides an excellent systematical description of hypernuclei. Effects of tensor coupling term on properties of Lambda hypernuclei, especially on delicate single particle properties, are also discussed.