1、CentOS安装Python的依赖包

yum groupinstall "Development tools"
yum install zlib-devel bzip2-devel openssl-devel ncurses-devel sqlite-devel readline-devel tk-devel gdbm-devel db4-devel libpcap-devel xz-devel

2、下载Python3.4的源码包并编译

wget https://www.python.org/ftp/python/3.4.1/Python-3.4.1.tgz
tar xf Python-3.4.1.tgz
cd Python-3.4.1
./configure --prefix=/usr/local --enable-shared
make
make install

3、在运行Python之前需要配置库：

echo /usr/local/lib >> /etc/ld.so.conf.d/local.conf
ldconfig

4、运行演示：

python3 --version
Python 3.4.1

5、删除编译Python时所需要的库

yum groupremove "Development tools" --remove-leaves
yum remove zlib-devel bzip2-devel openssl-devel ncurses-devel sqlite-devel readline-devel tk-devel gdbm-devel db4-devel libpcap-devel xz-devel --remove-leaves

参考
http://www.linuxidc.com/Linux/2015-01/111870.htm