The form factors of B(s) decays into P-wave excited charmed mesons (including D*
0(2300), D1(2430), D1(2420), D*
2(2460) and their strange counterparts, denoted generically as D**
(s)) are systematically calculated via the QCD sum rules in the framework of heavy quark
effective field theory (HQEFT). We consider contributions up to the next leading order of heavy quark expansion and give all the relevant form factors, including the scalar and tensor ones which are only related to possible new physics effects. The expressions of
 form factors in terms of several universal wave functions are derived via the heavy quark expansion. These universal functions can be evaluated through QCD sum rules. Then the numerical results of form factors are presented. With the form factors given here, a model independent analysis of relevant semileptonic decays B(s)→D**
(s) l νl is performed, including the contributions from possible new physics effects. Our predictions for the differential decay widths, branching fractions and the ratios of branching fractions R(D**
(s)) may be tested by more precise experiments in the future. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.