http://bicofino.io/2014/10/25/install-kernel-3-dot-10-on-centos-6-dot-5/
CentOS 6.5 ships with kernel 2.6 and it's a quite old for now(CentOS 7 already comes with 3.10), but compile a kernel on CentOS is a mess and it's not recommended. But fear no more, guys from Elrepo took care of that for us and made a package, let's see how we can install it.
Enable ELRepo Project repository
rpm –import https://www.elrepo.org/RPM-GPG-KEY-elrepo.org
rpm -Uvh http://www.elrepo.org/elrepo-release-6-6.el6.elrepo.noarch.rpm
Install the kernel
yum --enablerepo=elrepo-kernel install kernel-lt
Configure grub
You also need edit /etc/grub.conf ( your system is centos and can't find /etc/grub.conf ,try /boot/efi/EFI/redhat/grub.conf )to change the kernel order, change default from 1 to 0, must looks like the below:
default=0 timeout=5 splashimage=(hd0,0)/grub/splash.xpm.gz hiddenmenu title CentOS (3.10.55-1.el6.elrepo.x86_64) root (hd0,0) kernel /vmlinuz-3.10.55-1.el6.elrepo.x86_64 ro root=/dev/mapper/VolGroup-lv_root rd_NO_LUKS LANG=en_US.UTF-8 rd_NO_MD rd_LVM_LV=VolGroup/lv_swap SYSFONT=latarcyrheb-sun16 crashkernel=auto rd_LVM_LV=VolGroup/lv_root rd_NO_DM KEYBOARDTYPE=pc KEYTABLE=br-abnt2 rhgb quiet…
Reboot and profit!
reboot
Now you have a fresh(not so much) kernel on CentOS.
###20180105 ###notice
after update to lt 4.4 core
edit /etc/ssh/sshd_config
add UsePAM yes
or ssh will not get through
(some system doesn't have PAM model ,need yum update before kernel update)